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Almost sure asymptotic for Ornstein–Uhlenbeck processes of Poisson potential

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  • Xing, Fei
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    Abstract

    The objective of this paper is to study the large time asymptotic of the following exponential moment: Exexp{±∫0tV(X(s))ds}, where {X(s)} is a d-dimensional Ornstein–Uhlenbeck process and {V(x)}x∈Rd is a homogeneous ergodic random Poisson potential. It turns out that the positive/negative exponential moment has ect growth/decay rate, which is different from the Brownian motion model studied by Carmona and Molchanov (1995) for positive exponential moment and Sznitman (1993) for negative exponential moment.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 12 ()
    Pages: 2091-2102

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2091-2102

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    Related research

    Keywords: Ornstein–Uhlenbeck process; Poisson potential; Feynman–Kac formula; Principle eigenvalue;

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