Parameter estimation in mixed fractional stochastic heat equation
Volume 10, Issue 2 (2023), pp. 175–195
Pub. online: 24 January 2023
Type: Research Article
Open Access
Open Access
Received
8 August 2022
8 August 2022
Revised
29 November 2022
29 November 2022
Accepted
15 January 2023
15 January 2023
Published
24 January 2023
24 January 2023
Abstract
The paper is devoted to a stochastic heat equation with a mixed fractional Brownian noise. We investigate the covariance structure, stationarity, upper bounds and asymptotic behavior of the solution. Based on its discrete-time observations, we construct a strongly consistent estimator for the Hurst index H and prove the asymptotic normality for $H < 3/4$. Then assuming the parameter H to be known, we deal with joint estimation of the coefficients at the Wiener process and at the fractional Brownian motion. The quality of estimators is illustrated by simulation experiments.
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