Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation

Abstract

The paper deals with a stochastic heat equation driven by an additive fractional Brownian space-only noise. We prove that a solution to this equation is a stationary and ergodic Gaussian process. These results enable us to construct a strongly consistent estimator of the diffusion parameter.

Keywords

• Stochastic partial differential equation
• fractional Brownian motion
• stationary process
• ergodic process
• strong consistency