Spectral analysis for some multifractional Gaussian processes
A.I. Karol, A.I. Nazarov
TL;DR
This paper investigates the small ball probabilities in L2 for generalized multifractional Gaussian processes with variable Hurst parameters, using spectral analysis of related integral operators.
Contribution
It provides a detailed spectral analysis of integral operators associated with these processes, advancing understanding of their small deviation behavior.
Findings
Derived asymptotics for singular values of integral operators
Established small ball probability estimates for multifractional Gaussian processes
Extended classical results to variable Hurst parameter cases
Abstract
We study the small ball asymptotics problem in for two generalizations of the fractional Brownian motion with variable Hurst parameter. To this end, we perform careful analysis of the singular values asymptotics for associated integral operators.
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