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We develop connections between Stein's approximation method, logarithmic Sobolev and transport inequalities by introducing a new class of functional inequalities involving the relative entropy, the Stein kernel, the relative Fisher…

Probability · Mathematics 2014-07-24 Michel Ledoux , Ivan Nourdin , Giovanni Peccati

In this article, we will construct an approximation of Gaussian white noise based on the sequence of Bernoulli random variables and define Wick's products and the stochastic exponent for the Bernoulli case. Here we will propose a method to…

Probability · Mathematics 2023-04-20 Anastasiia Hrabovets

We propose a new version of Stein's method of exchangeable pairs, which, given a suitable exchangeable pair $(W,W')$ of real-valued random variables, suggests the approximation of the law of $W$ by a suitable absolutely continuous…

Probability · Mathematics 2015-10-21 Christian Döbler

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a…

Probability · Mathematics 2012-01-27 Zachary Gelbaum

We investigate Stein-Malliavin approximations for nonlinear functionals of geometric interest of Gaussian random eigenfunctions on the unit $d$ -dimensional sphere ${\mathbb{S}}^{d},$ $d\geq 2.$ All our results are established in the high…

Probability · Mathematics 2015-04-29 Domenico Marinucci , Maurizia Rossi

We consider random multiplicative functions taking the values $\pm 1$. Using Stein's method for normal approximation, we prove a central limit theorem for the sum of such multiplicative functions in appropriate short intervals.

Number Theory · Mathematics 2011-02-03 Sourav Chatterjee , Kannan Soundararajan

We consider the Gittins index for a normal distribution with unknown mean $\theta$ and known variance where $\theta$ has a normal prior. In addition to presenting some monotonicity properties of the Gittins index, we derive an approximation…

Statistics Theory · Mathematics 2007-06-13 Yi-Ching Yao

This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…

Probability · Mathematics 2023-12-08 Pratima Eknath Kadu

The concepts of Hamiltonian Feynman integrals in white noise analysis are used to realize as the first velocity dependent potential the Hamiltonian Feynman integrand for a charged particle in a constant magnetic field in coordinate space as…

Mathematical Physics · Physics 2016-01-26 Wolfgang Bock , Martin Grothaus

In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability is modified. This modification can be understood as a…

Analysis of PDEs · Mathematics 2017-11-21 Romain Duboscq , Anthony Réveillac

We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters…

Numerical Analysis · Mathematics 2024-05-17 Andrea Bonito , Diane Guignard , Wenyu Lei

We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…

Probability · Mathematics 2012-04-18 Giovanni Peccati

We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when the solution is sampled discretely in the physical domain.…

Probability · Mathematics 2021-07-15 Igor Cialenco , Hyun-Jung Kim

We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…

Probability · Mathematics 2015-11-24 Christian Döbler

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…

Optimization and Control · Mathematics 2021-03-05 Albert S. Berahas , Liyuan Cao , Katya Scheinberg

We consider the normal approximation of Kabanov-Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov-Skorohod…

Probability · Mathematics 2023-09-06 Günter Last , Ilya Molchanov , Matthias Schulte

This paper is concerned with linear stochastic systems whose output is a stationary Gaussian random process related by an integral operator to a standard Wiener process at the input. We consider a performance criterion which involves the…

Optimization and Control · Mathematics 2022-04-28 Igor G. Vladimirov , Ian R. Petersen

In this paper, we extend Walsh's stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns…

Probability · Mathematics 2007-05-23 David Nualart , Lluis Quer-Sardanyons

We consider $M/Ph/n+M$ queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein-Uhlenbeck (OU) process is bounded by…

Probability · Mathematics 2015-12-01 Anton Braverman , J. G. Dai

We formulate an initial- and Dirichlet boundary- value problem for a linear stochastic heat equation, in one space dimension, forced by an additive space-time white noise. First, we approximate the mild solution to the problem by the…

Numerical Analysis · Mathematics 2017-09-26 Georgios E. Zouraris