Parameter estimation in mixed fractional stochastic heat equation

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. 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

• Stochastic partial differential equation
• mixed fractional Brownian motion
• Hurst index estimation
• strong consistency
• Asymptotic normality