Exact Temporal Variation for Fractional Stochastic Heat Equation Driven by Space-Time White Noise

TL;DR

This paper investigates the precise temporal variation of solutions to a fractional stochastic heat equation driven by space-time white noise, providing insights into its behavior and estimating the drift parameter.

Contribution

It introduces an exact analysis of the fractional variation of the solution's temporal process and offers a method to estimate the drift parameter.

Findings

Derived the exact fractional variation for the solution's temporal process

Provided an estimate for the drift parameter in the model

Enhanced understanding of stochastic heat equations driven by space-time white noise

Abstract

In this paper, we consider the exact fractional variation for the temporal process of the solution to the fractional stochastic heat equation on $\mathbb{R}$ driven by a space-time white noise, and as an application we give the estimate of drift parameter.