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

Alexander I. Nazarov

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arXiv · 1908.10299

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

Alexander I. Nazarov

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Abstract

We study 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 eigenvalue asymptotics for such equations. Application to the small ball probabilities in $L_2$-norm is given.

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BibTeX RIS

Alexander I. Nazarov. 2019-08-27. Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes. https://arxiv.org/abs/1908.10299

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