Pseudo-Likelihood Estimation for Parameters of Stochastic Time-Fractional Diffusion Equations

Abstract

Although stochastic fractional partial differential equations have received increasing attention in the last decade, the parameter estimation of these equations has been seldom reported in literature. In this paper, we propose a pseudo-likelihood approach to estimating the parameters of stochastic time-fractional diffusion equations, whose forward solver has been investigated very recently by Gunzburger, Li, and Wang (2019). Our approach can accurately recover the fractional order, diffusion coefficient, as well as noise magnitude given the discrete observation data corresponding to only one realization of driving noise. When only partial data is available, our approach can also attain acceptable results for intermediate sparsity of observation.

Keywords

• parameter estimation
• stochastic PDE
• fractional diffusion
• fractional derivative
• maximum likelihood estimation
• pseudo-likelihood approach