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Almost sure asymptotic for Ornstein–Uhlenbeck processes of Poisson potential

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  • Xing, Fei

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.

Suggested Citation

  • Xing, Fei, 2012. "Almost sure asymptotic for Ornstein–Uhlenbeck processes of Poisson potential," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2091-2102.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2091-2102
    DOI: 10.1016/j.spl.2012.07.012
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