On a space discretization scheme for the Fractional Stochastic Heat Equations

TL;DR

This paper introduces a new discretization scheme for the fractional Laplacian and develops an approximation method for fractional heat equations with multiplicative noise, including convergence rate analysis.

Contribution

The work presents a novel discretization approach for the fractional Laplacian and applies it to stochastic heat equations with noise, providing convergence estimates.

Findings

New discretization scheme for fractional Laplacian

Approximation method for stochastic fractional heat equations

Convergence rate estimates for the scheme

Abstract

In this work, we introduce a new discretization to the fractional Laplacian and use it to elaborate an approximation scheme for fractional heat equations perturbed by a multiplicative cylindrical white noise. In particular, we estimate the rate of convergence.