Parameter estimation in mixed fractional stochastic heat equation
Open Access
- 24 January 2023
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 10 (2), 175-195
- https://doi.org/10.15559/23-vmsta221
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Parameter estimation in mixed fractional stochastic heat equation, Authors: Diana Avetisian, Kostiantyn Ralchenko , 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.
Keywords
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