Approximations for a solution to stochastic heat equation with stable noise

TL;DR

This paper studies a stochastic heat equation driven by a stable noise process and demonstrates that solutions approximated by truncating a LePage series converge to the true solution.

Contribution

It introduces a method of approximating solutions to the stochastic heat equation with stable noise via LePage series truncation and proves convergence.

Findings

Convergence of truncated LePage series approximations to the true solution

Effective approximation method for stochastic heat equations with stable noise

Theoretical validation of approximation accuracy

Abstract

We consider a Cauchy problem for stochastic heat equation driven by a real harmonizable fractional stable process $Z$ with Hurst parameter $H>1/2$ and stability index $\alpha>1$. It is shown that the approximations for its solution, which are defined by truncating the LePage series for $Z$, converge to the solution.