Jaya P. N. Bishwal
Approximate Maximum Likelihood Estimation in Semilinear SPDE
Dynamic Systems and Applications 32 (2023) 165-188

https://doi.org/10.46719/dsa2023.32.10

ABSTRACT.
We estimate the drift in the semilinear SPDE by approximation by space and time discretization. We study the asymptotic properties of the approximate maximum likelihood estimators and also the rates of convergence. We also study parameter estimation in controlled semilinear SPDE.

AMS (MOS) Subject Classification. 35R60, 37H15, 37L55, 60G44, 60H10, 60H15, 60H35, 60J60, 62M05, 62M99, 62F12, 65L09, 93E20.

Key Words and Phrases. Semilinear SPDE, time and space discretization, finite-element method, Galerkin approximation, Crank-Nicholson scheme, Euler scheme, rate of convergence, Markov control, admissibility, approximate maximum likelihood estimation, consistency, asymptotic normality.