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 timevarying coefficient 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 coefficient and the convergence rates. An example is given to illustrate the theorem.

Keywords

Fractional white noise / elliptic partial differential operator / kernel estimator

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