Weak approximation of the fractional Brownian sheet from random walks

Zhi Wang,Xianye Yu,Litan Yan

doi:10.1214/ecp.v18-2878

Abstract

In this paper, we show an approximation in law of the fractional Brownian sheet by random walks. As an application, we consider a quasilinear stochastic heat equation with Dirichlet boundary conditions driven by an additive fractional noise.

Highlights

Introduction and main resultGiven α, β ∈ (0, 1), a fractional Brownian sheet on R is a two-parameter centered Gaussian processW α, β = {W α, β(t, s), (t, s) ∈ R2+} such that EW α, β(t, s)W α, β(t, s ) 1 =t2α + t 2α − |t − t|2α 1 ·s2β + s 2β − |s − s|2β For α =
We show an approximation in law of the fractional Brownian sheet by random walks
We consider a quasilinear stochastic heat equation with Dirichlet boundary conditions driven by an additive fractional noise

Summary

Introduction

We show an approximation in law of the fractional Brownian sheet by random walks. Β ∈ (0, 1), a fractional Brownian sheet on R is a two-parameter centered Gaussian process As an application of Theorem 1.1, in Section 3 we consider the approximation solution of a one-dimensional quasi-linear stochastic heat equation driven by fractional noise.

Results

Conclusion