Theory of Probability and Mathematical Statistics
Estimation of the Hurst and diffusion parameters in fractional stochastic heat equation
D.A. Avetisian, K.V. Palchenko
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Abstract: The paper deals with a one-dimensional stochastic heat equation driven by a space-only fractional Brownian noise. We construct strongly consistent estimators of two unknown parameters, namely, the diffusion parameter $\sigma$ and the Hurst parameter $H\in(0,1)$, based on the discrete-time observations of a solution. We also prove joint asymptotic normality of the estimators in the case $H\in\left (0,\frac34\right )$.
Keywords: Stochastic partial differential equation, fractional Brownian motion, strong consistency, asymptotic normality
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