Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes

Abstract

We study the spectral problems for integro-differential equations arising in the theory of Gaussian processes similar to the fractional Brownian motion. We generalize the method of Chigansky-Kleptsyna and obtain the two-term eigenvalues asymptotics for such equations. Application to the small ball probabilities in L 2 -norm is given.