Gaussian fluctuations for the wave equation under rough random perturbations

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-01-16 DOI:10.1016/j.spa.2025.104569

Raluca M. Balan , Jingyu Huang , Xiong Wang , Panqiu Xia , Wangjun Yuan

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引用次数: 0

Abstract

In this article, we consider the stochastic wave equation in spatial dimension

d = 1

, with linear term

σ (u) = u

multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with Hurst index

H \in (\frac{1}{4}, \frac{1}{2})

. First, we prove that the solution is strictly stationary and ergodic in the spatial variable. Then, we show that with proper normalization and centering, the spatial average of the solution converges to the standard normal distribution, and we estimate the rate of this convergence in the total variation distance. We also prove the corresponding functional convergence result.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.