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- W2512738247 abstract "Many results in theory of Gaussian processes rely on the spectral structure of covariance operator, which is often hard to reveal in a closed form. In this paper we consider eigenproblems for the fractional Brownian motion and its formal derivative, the fractional noise, and obtain accurate asymptotic approximations both for the eigenvalues and the eigenfunctions. Our results provide a key to several problems, whose solution is long known in the standard Brownian case, but was missing in the more general fractional setting. This includes computation of the exact limits of $L^2$-small ball probabilities and asymptotic analysis of singularly perturbed integral equations, arising in mathematical physics and applied probability." @default.
- W2512738247 created "2016-09-16" @default.
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- W2512738247 date "2016-01-21" @default.
- W2512738247 modified "2023-10-06" @default.
- W2512738247 title "Exact asymptotics in eigenproblems with fractional Brownian covariance operators" @default.
- W2512738247 hasPublicationYear "2016" @default.
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