Central limit theorems for heat equation with time-independent noise: the regular and rough cases

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-05-26 DOI:10.1142/s0219025722500291

R. Balan, Wangjun Yuan

引用次数: 3

Abstract

In this article, we investigate the asymptotic behaviour of the spatial integral of the solution to the parabolic Anderson model with time independent noise in dimension d ≥ 1, as the domain of the integral becomes large. We consider 3 cases: (a) the case when the noise has an integrable covariance function; (b) the case when the covariance of the noise is given by the Riesz kernel; (c) the case of the rough noise, i.e. fractional noise with index H ∈ ( 14 , 12 ) in dimension d = 1. In each case, we identify the order of magnitude of the variance of the spatial integral, we prove a quantitative central limit theorem for the normalized spatial integral by estimating its total variation distance to a standard normal distribution, and we give the corresponding functional limit result.

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含时无关噪声热方程的中心极限定理:正则和粗糙情况

在本文中，我们研究了d≥1维具有时间无关噪声的抛物型Anderson模型解的空间积分随着积分域变大时的渐近行为。我们考虑了3种情况:(a)噪声具有可积协方差函数的情况;(b)噪声的协方差由Riesz核给出的情况;(c)粗糙噪声的情况，即d = 1维的指数H∈(14,12)的分数噪声。在每种情况下，我们确定了空间积分方差的数量级，通过估计其到标准正态分布的总变异距离证明了归一化空间积分的定量中心极限定理，并给出了相应的函数极限结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.