Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation
Volume 7, Issue 3 (2020), pp. 339–356
Pub. online: 18 September 2020
Type: Research Article
Open Access
Open Access
Received
11 May 2020
11 May 2020
Revised
2 August 2020
2 August 2020
Accepted
11 September 2020
11 September 2020
Published
18 September 2020
18 September 2020
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.
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