Asymptotic analysis of a kernel estimator for parabolic stochastic partial differential equations driven by fractional noises

Abstract

We study a strongly elliptic partial differential operator with time-varying coeffcient in a parabolic diagonalizable stochastic equation driven by fractional noises. Based on the existence and uniqueness of the solution, we then obtain a kernel estimator of time-varying coeffcient and the convergence rates. An example is given to illustrate the theorem.