Exact L₂-small ball asymptotics of Gaussian processes and the spectrum of boundary value problems with "non-separated" boundary conditions

2007/10/07 by Alexander I. Nazarov, A. I. Nazarov, Nazarov, A. I.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #advanced mathematical theories #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.0710.1408

arxiv created 2007/10/07 · arxiv updated 2009/12/01

Abstract

We sharpen a classical result on the spectral asymptotics of the boundary value problems for self-adjoint ordinary differential operator. Using this result we obtain the exact L₂-small ball asymptotics for a new class of zero mean Gaussian processes. This class includes, in particular, integrated generalized Slepian process, integrated centered Wiener process and integrated centered Brownian bridge.

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