Wick-type stochastic parabolic equations with random potentials

TL;DR

This paper investigates Wick-type stochastic parabolic equations with random potentials, establishing existence, uniqueness, and coefficient estimates of solutions using chaos expansion in white noise analysis.

Contribution

It introduces a framework for solving stochastic parabolic equations with random potentials using Wick products and chaos expansion, providing new existence and uniqueness results.

Findings

Existence and uniqueness of solutions proved.

Coefficient estimates in chaos expansion provided.

Framework applicable to equations with random potentials.

Abstract

The stochastic parabolic equations with random potentials, driving forces and initial conditions are considered. The Wick product is used to give sense to the product of two generalized stochastic processes, and the existence and uniqueness of solutions are proved via the chaos expansion method from white noise analysis. The estimates on coefficients in the chaos expansion form of the solutions are provided.