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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 3, Pages 203–224 (Mi izv6594)  

This article is cited in 1 scientific paper (total in 1 paper)

Negative-order moments for $L^p$-functionals of Wiener processes: exact asymptotics

V. R. Fatalov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove theorems on the exact asymptotics as $T \to \infty$ of the integrals $\mathsf{E}[\frac{1}{T}\int_0^T|\eta(t)|^pdt]^{-T}$, $p>0$, for two stochastic processes $\xi(t)$, the Wiener process and the Brownian bridge, as well as for their conditional versions. We also obtain a number of related results. We shall use the Laplace method for the occupation times of homogeneous Markov processes. We write the constants in our exact asymptotic formulae explicitly in terms of the minimal eigenvalue and corresponding eigenfunction for the Schrödinger operator with a potential of polynomial type.

Keywords: large deviations, occupaton time of Markov processes, Schrödinger operator, action functional, Fréchet differentiation.

DOI: https://doi.org/10.4213/im6594

Full text: PDF file (662 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:3, 626–646

Bibliographic databases:

UDC: 519.2
MSC: 60F10, 60J05, 60J65
Received: 28.12.2010

Citation: V. R. Fatalov, “Negative-order moments for $L^p$-functionals of Wiener processes: exact asymptotics”, Izv. RAN. Ser. Mat., 76:3 (2012), 203–224; Izv. Math., 76:3 (2012), 626–646

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. R. Fatalov, “Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for $L^p$-functionals, $0<p<\infty$”, Problems Inform. Transmission, 50:4 (2014), 371–389  mathnet  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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