Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes-Reference-Cited by-同舟云学术

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

Published:2020-08-28 Issue:06 Volume:23 Page:2050049
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Nazarov Alexander I.¹²

Affiliation:

1. St.Petersburg Department of Steklov Institute, Fontanka 27, St.Petersburg 191023, Russia

2. St.Petersburg State University, Universitetskii pr. 28, St.Petersburg 198504, Russia

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 [Formula: see text]-norm is given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199720500492

Reference16 articles.

1. Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory

2. Exact asymptotics in eigenproblems for fractional Brownian covariance operators

3. On the eigenproblem for Gaussian bridges

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