Parameter estimation in mixed fractional stochastic heat equation

• Published in: Modern Stochastics: Theory and Applications Vol. 10; no. 2; pp. 175 - 195
• Main Authors: Diana Avetisian, Kostiantyn Ralchenko
• Format: Journal Article
• Language: English
• Published: VTeX 01-04-2023
• Subjects: Asymptotic normality; Hurst index estimation; mixed fractional Brownian motion; Stochastic partial differential equation; strong consistency
• ISSN: 2351-6046; 2351-6054
• DOI: 10.15559/23-VMSTA221

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. 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.