Inverse Problems for Stochastic PDEs Driven by Multiplicative Fractional Noise
Department of Applied Mathematics
Illinois Institute of Technology
We will focus on estimating the drift coefficient and the Hurst parameter for some parabolic SPDEs driven by multiplicative fractional noise. Using the singularity of the probability measures generated by the solutions (for different parameters) we propose two sets of estimates: maximum likelihood based estimates for the drift coefficient and a new class of estimates called “exact estimates” for drift and Hurst parameter. For these estimates we study standard efficiency, asymptotic normality. Finally we will discuss some numerical examples.