2020/03/19 by Igor Cialenco, Cialenco, Igor, Hyun-Jung Kim +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Statistical Methods and Inference #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2003.08920
We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when the solution is sampled discretely in the physical domain. We consider both the full space and the bounded domain. We establish the exact spatial regularity of the solution, which in turn, using power-variation arguments, allows building the desired estimators. We show that naive approximations of the derivatives appearing in the power-variation based estimators may create nontrivial biases, which we compute explicitly. The proofs are rooted in Malliavin-Stein's method.