76
76
Oct 6, 2015
10/15
by
Tovey, Craig A.
texts
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Title from cover
Topic: PROBABILITY.
This course focuses on Modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic...
Topic: probability
7
7.0
Mar 1, 2022
03/22
by
Pfeiffer, Paul E
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comment 0
xiii, 403 pages 25 cm
Topics: Probabilities, Probability, Probabilités, probability, Wahrscheinlichkeitsrechnung
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6.0
web
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Probability-Project dumped with WikiTeam tools.
Topics: wiki, wikiteam, wikispaces, Probability-Project, probability-project,...
London School of Hygiene & Tropical Medicine Library & Archives Service
Topic: Probability
Title from cover
Topic: PROBABILITY.
87
87
Nov 18, 2015
11/15
by
F. Smarandache
texts
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In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy”.
Topics: imprecise probability, neutrosophic probability, neutrosophic logic
71
71
Nov 18, 2015
11/15
by
Florentin Smarandache
texts
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In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy”.
Topics: imprecise probability, neutrosophic probability, neutrosophic logic
442
442
Nov 14, 2013
11/13
by
Charles E. Leiserson
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Abstract: This tutorial teaches dynamic multithreaded algorithms using a Cilk-like [11, 8, 10] model. The material was taught in the MIT undergraduate class 6.046 Introduction to Algorithms as two 80-minute lectures. The style of the lecture notes follows that of the textbook by Cormen, Leiserson, Rivest, and Stein [7], but the pseudocode from that textbook has been �Cilki�ed� to allow it to describe multithreaded algorithms. The �rst lecture teaches the basics behind multithreading,...
Topics: Maths, Statistics and Probability, Probability, Mathematics
Source: http://www.flooved.com/reader/1567
162
162
Nov 14, 2013
11/13
by
Erik Demaine
texts
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Topics: Maths, Statistics and Probability, Probability, Mathematics
Source: http://www.flooved.com/reader/1568
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3.0
texts
eye 3
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comment 0
1 vol. (VIII-410 p.) ; 24 cm
Topics: Probabilities, Probability, Probabilités, probability, Processus stochastiques
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38
Sep 20, 2016
09/16
by
Petrov, A. A.
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comment 0
Topics: Statistics, Probability
4
4.0
Jun 29, 2018
06/18
by
A. Kozhina
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We study the sensitivity of the densities of some Kolmogorov like degenerate diffusion processes with respect to a perturbation of the coefficients of the non-degenerate component. Under suitable (quite sharp) assumptions we quantify how the pertubation of the SDE affects the density. Natural applications of these results appear in various fields from mathematical finance to kinetic models.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1602.04770
4
4.0
Jun 29, 2018
06/18
by
Nicole El Karoui; Anis Matoussi; Armand Ngoupeyou
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In this paper, we study a class of Quadratic Backward Stochastic Differential Equations (QBSDE in short) with jumps and unbounded terminal condition. We extend the class of quadratic semimartingales introduced by Barrieu and El Karoui (2013) in the jump diffusion model. The properties of these class of semimartingales lead us to prove existence result for the solution of a quadratic BSDEs.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1603.06191
4
4.0
Jun 29, 2018
06/18
by
Thomas Courtat; Laurent Decreusefond; Phillipe Martins
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We are interested in the assessment of electromagnetic Path-Loss in complex environments. The Path-loss is the attenuation function $P$ of the electromagnetic power at a distance $d$ of an antenna. In free-space, $P(d) \propto 1/d^2$, in complex environments like cities, wave trajectory is altered by successive reflections and absorptions, the path-loss is not theoretically known and engineering rules postulate that $P(d) \simeq 1/d^{\gamma}, \, \gamma>2$. We place in a stochastic geometry...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1604.00688
4
4.0
Jun 29, 2018
06/18
by
Dmitry Ostrovsky
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A new family of Barnes beta distributions on $(0, \infty)$ is introduced and its infinite divisibility, moment determinacy, scaling, and factorization properties are established. The Morris integral probability distribution is constructed from Barnes beta distributions of types $(1,0)$ and $(2,2),$ and its moment determinacy and involution invariance properties are established. For application, the maximum distributions of the 2D gaussian free field on the unit interval and circle with a...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1605.01589
3
3.0
Jun 29, 2018
06/18
by
Amites Dasgupta; Mahuya Datta
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Starting with a short map $f_0:I\to \mathbb R^3$ on the unit interval $I$, we construct random isometric map $f_n:I\to \mathbb R^3$ (with respect to some fixed Riemannian metrics) for each positive integer $n$, such that the difference $(f_n - f_0)$ goes to zero in the $C^0$ norm. The construction of $f_n$ uses the Nash twist. We show that the distribution of $ n^{1/2} (f_n - f_0)$ converges (weakly) to a Gaussian noise measure.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1605.02421
3
3.0
Jun 29, 2018
06/18
by
Lassi Päivärinta; Petteri Piiroinen
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In this paper, we study the recovery of the Hurst parameter from a given discrete sample of fractional Brownian motion with statistical inverse theory. In particular, we show that in the limit the posteriori distribution of the parameter given the sample determines the parameter uniquely. In order to obtain this result, we first prove various strong laws of large numbers related to the problem at hand and then employ these limit theorems to verify directly the limiting behaviour of posteriori...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1606.07576
3
3.0
Jun 29, 2018
06/18
by
Peng Liu; Chunsheng Zhang; Lanpeng Ji
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In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1608.05514
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6.0
Jun 29, 2018
06/18
by
Marc Lelarge; Léo Miolane
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We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean square error, while the rank of the signal remains constant. We also show that our model extends beyond the particular case of additive...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1611.03888
5
5.0
Jun 29, 2018
06/18
by
Xiequan Fan
texts
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We improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variables, we also refine the convergence rate function of McDiarmid's inequality around a median. Moreover, a non-uniform bound for the distance between the medians and the mean is also given. We also give some extensions of McDiarmid's inequalities to the case of nonnegative functionals of dependent random variables.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1611.03990
3
3.0
Jun 30, 2018
06/18
by
Dan Crisan; Eamon McMurray
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In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1702.01397
3
3.0
Jun 30, 2018
06/18
by
Madalina Deaconu; Samuel Herrmann
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In this paper we pursue and complete the study of the simulation of the hitting time of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work, the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method was based mainly on the explicit formula for the distribution of the hitting time and on the connexion between the Bessel...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1401.4843
3
3.0
Jun 30, 2018
06/18
by
Shiqi Song
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The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an existence of a density function for the conditional law of the random times will not be enough for the purposes of some numerical implantation problems. It becomes necessary to have models with martingales of density functions evolving along with the...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1401.6909
3
3.0
Jun 30, 2018
06/18
by
Piotr Graczyk; Salha Mamane
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We consider natural and general exponential families $(Q_m)_{m\in M}$ on $\mathbb{R}^d$ parametrized by the means. We study the submodels $(Q_{\theta m_1+(1-\theta)m_2})_{\theta\in[0,1]}$ parametrized by a segment in the means domain, mainly from the point of view of the Fisher information. Such a parametrization allows for a parsimonious model and is particularly useful in practical situations when hesitating between two parameters $m_1$ and $m_2$. The most interesting examples are obtained...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1402.1305
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11
Jun 30, 2018
06/18
by
Waly Ngom
texts
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We study the default risk in incomplete information. That means, we model the value of a firm by one L\'evy process which is the sum of brownian motion with drift and compound Poisson process. This L\'evy process can not be observed completely and we let an other process which representes the available information on the firm. We obtain an equation safisfied by the conditional density of the default time given the available information and closed form expression for the density.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1402.2000
3
3.0
Jun 30, 2018
06/18
by
A. D. Barbour; A. Collevecchio
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We consider the motion of a particle on a Galton Watson tree, when the probabilities of jumping from a vertex to any one of its neighbours is determined by a random process. Given the tree, positive weights are assigned to the edges in such a way that, viewed along any line of descent, they evolve as a random process. In order to introduce our method for proving transience or recurrence, we first suppose that the weights are i.i.d., reproving a result of Lyons and Pemantle. We then extend the...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1402.4163
3
3.0
Jun 30, 2018
06/18
by
Stefano Bonaccorsi; Sonia Mazzucchi
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eye 3
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A probabilistic construction for the solution of a general class of high order heat-type equations is constructed in terms of the scaling limit of random walks in the complex plane.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1402.6140
5
5.0
Jun 30, 2018
06/18
by
F. Götze; A. Yu. Zaitsev
texts
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We estimate the concentration functions of $n$-fold convolutions of one-dimensional probability measures. The main result is a supplement to the results of G\"otze and Zaitsev (1998). We show that the estimation of concentration functions at arguments of bounded size can be reduced to the estimation of these functions at arguments of size $O(\sqrt n)$ which is easier.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1402.6966
3
3.0
Jun 30, 2018
06/18
by
Jinghai Shao
texts
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Based on the theory of M-matrix and Perron-Frobenius theorem, we provide some criteria to justify the convergence of the regime-switching diffusion processes in Wasserstein distances. The cost function we used to define the Wasserstein distance is not necessarily bounded. The continuous time Markov chains with finite and countable state space are all studied. To deal with the countable state space, we put forward a finite partition method. The boundedness for state-dependent regime-switching...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1403.0291
5
5.0
Jun 30, 2018
06/18
by
Masanori Hino
texts
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We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1403.3151
3
3.0
Jun 30, 2018
06/18
by
H. A. Mardones; C. M. Mora
texts
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We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes for multidimensional bilinear SDEs achieving the first order of weak convergence, which do not involve multiple stochastic integrals. To this end, we follow two methodologies to find appropriate stabilizing weights; through an optimization procedure or based...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1403.6142
3
3.0
Jun 30, 2018
06/18
by
Yueyun Hu; Zhan Shi
texts
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Biased random walks on supercritical Galton--Watson trees are introduced and studied in depth by Lyons (1990) and Lyons, Pemantle and Peres (1996). We investigate the slow regime, in which case the walks are known to possess an exotic maximal displacement of order $(\log n)^3$ in the first $n$ steps. Our main result is another --- and in some sense even more --- exotic property of biased walks: the maximal potential energy of the biased walks is of order $(\log n)^2$. More precisely, we prove...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1403.6799
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4.0
Jun 30, 2018
06/18
by
Federica Masiero
texts
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We consider a backward stochastic differential equation in a Markovian framework for the pair of processes $(Y,Z)$, with generator with quadratic growth with respect to $Z$. Under non-degeneracy assumptions, we prove an analogue of the well-known Bismut-Elworty formula when the generator has quadratic growth with respect to $Z$. Applications to the solution of a semilinear Kolmogorov equation for the unknown $v$ with nonlinear term with quadratic growth with respect to $\nabla v$ and final...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1404.2098
4
4.0
Jun 30, 2018
06/18
by
Kevin Leckey; Ralph Neininger; Henning Sulzbach
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The complexity of the algorithm Radix Selection is considered for independent data generated from a Markov source. The complexity is measured by the number of bucket operations required and studied as a stochastic process indexed by the ranks; also the case of a uniformly chosen rank is considered. The orders of mean and variance of the complexity and limit theorems are derived. We find weak convergence of the appropriately normalized complexity towards a Gaussian process with explicit mean and...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1404.3672
3
3.0
Jun 30, 2018
06/18
by
Romain Couillet
texts
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A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random matrix models. It is precisely shown that, as opposed to sample covariance matrices which may have asymptotically unbounded (eigen-)spectrum due to the sample impulsiveness, the robust estimator of scatter has bounded spectrum and may contain isolated eigenvalues...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1404.7685
3
3.0
Jun 30, 2018
06/18
by
Manon Defosseux
texts
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We construct a sequence of Markov processes on the set of dominant weights of the Affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ which involves tensor product of irreducible highest weight modules of $\hat{\mathfrak{sl}_2}(\C)$ and show that it converges towards a Doob's space-time harmonic transformation of a space-time Brownian motion.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1401.3115
3
3.0
Jun 30, 2018
06/18
by
Nizar Demni
texts
eye 3
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Let $(U_t)_{t \geq 0}$ be a Brownian motion valued in the complex projective space $\mathbb{C}P^{N-1}$. Using unitary spherical harmonics of homogeneous degree zero, we derive the densities of $|U_t^{1}|^2$ and of $(|U_t^{1}|^2, |U_t^2|^2)$, and express them through Jacobi polynomials in the simplices of $\mathbb{R}$ and $\mathbb{R}^2$ respectively. More generally, the distribution of $(|U_t^{1}|^2, \dots, |U_t^k|^2), 2 \leq k \leq N-1$ may be derived using the decomposition of the unitary...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1403.3227
5
5.0
Jun 30, 2018
06/18
by
Radu V. Craiu; Lawrence Gray; Krzysztof Łatuszyński; Neal Madras; Gareth O. Roberts; Jeffrey S. Rosenthal
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We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and prove theorems to show that the answer is yes under various additional assumptions. We then use our results to prove convergence of various adaptive Markov chain Monte Carlo algorithms.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1403.3950
3
3.0
Jun 30, 2018
06/18
by
Tomoyuki Ichiba; Ioannis Karatzas
texts
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The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009). This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1404.4662
4
4.0
Jun 30, 2018
06/18
by
Mathew Joseph; Davar Khoshnevisan; Carl Mueller
texts
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We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1404.6911
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4.0
Jun 30, 2018
06/18
by
Eleni Vatamidou; Ivo J. B. F. Adan; Maria Vlasiou; Bert Zwart
texts
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Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume that the claim sizes are a mixture of a phase-type and a heavy-tailed distribution and with the aid of perturbation analysis we derive a series expansion for the performance measure under consideration....
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1404.6411
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6.0
Jun 30, 2018
06/18
by
Panki Kim; Renming Song; Zoran Vondraček
texts
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Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness at finite and infinite minimal Martin boundary points for a large class of purely discontinuous symmetric L\'evy processes.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1405.0297
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5.0
Jun 30, 2018
06/18
by
Mikhail Lifshits; Eric Setterqvist
texts
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Let $W$ be a Wiener process. The function $h(\cdot)$ minmizing energy $\int_0^T h'(t)^2\, dt$ among all functions satisfying $W(t)-r \le h(t) \le W(t)+ r$ on an interval $[0,T]$ is called taut string. This is a classical object well known in Variational Calculus, Mathematical Statistics, etc. We show that the energy of this taut string on large intervals is equivalent to $C^2 T\, /\, r^2$ where $C$ is some finite positive constant. While the precise value of $C$ remains unknown, we give various...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1405.1651
4
4.0
Jun 30, 2018
06/18
by
Andrei N. Frolov
texts
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We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type inequalities, some other new bounds and a combinatorial central limit theorem in the case of infinite variations.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1405.1670
3
3.0
Jun 30, 2018
06/18
by
Nicolas Fournier; Eva Löcherbach
texts
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We continue the study of a stochastic system of interacting neurons introduced in De Masi-Galves-L\"ocherbach-Presutti (2014). The system consists of N neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset to 0 and all other neurons receive an additional amount 1/N of potential. Moreover, electrical synapses induce a deterministic drift of the system towards its center of mass. We prove propagation of chaos of the...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1410.3263
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7.0
Jun 30, 2018
06/18
by
Shui Feng; Feng-Yu Wang
texts
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The dimension-free Harnack inequality and uniform heat kernel upper/lower bounds are derived for a class of infinite-dimensional GEM processes, which was introduced in \cite{FW} to simulate the two-parameter GEM distributions. In particular, the associated Dirichlet form satisfies the super log-Sobolev inequality which strengthens the log-Sobolev inequality derived in \cite{FW}. To prove the main results, explicit Harnack inequality and super Poincar\'e inequality are established for the...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1410.3936
4
4.0
Jun 30, 2018
06/18
by
Martin Grothaus; Robert Voßhall
texts
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Using Girsanov transformations we construct from sticky reflected Brownian motion on $[0,\infty)$ a conservative diffusion on $E:=[0,\infty)^n$, $n \in \mathbb{N}$, and prove that its transition semigroup possesses the strong Feller property for a specified general class of drift functions. By identifying the Dirichlet form of the constructed process, we characterize it as sticky reflected distorted Brownian motion. In particular, the relations of the underlying analytic Dirichlet form methods...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1410.6040
5
5.0
Jun 30, 2018
06/18
by
Zsolt Nika; Tamás Szabados
texts
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A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973 (BSM model). A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979 (CRR model). The BSM and the CRR models have been used for example to price European call and put options. Our aim in this work is to give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks....
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1411.0501
3
3.0
Jun 30, 2018
06/18
by
Nicoletta Gabrielli; Josef Teichmann
texts
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Based on the theory of multivariate time changes for Markov processes, we show how to identify affine processes as solutions of certain time change equations. The result is a strong version of a theorem presented by J. Kallsen (2006) which provides a representation in law of an affine process as a time-change transformation of a family of independent L\'evy processes.
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1412.7837
