Almost sure asymptotic for Ornstein–Uhlenbeck processes of Poisson potential

Fei Xing

Statistics & Probability Letters, 2012, vol. 82, issue 12, 2091-2102

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.

Keywords: Ornstein–Uhlenbeck process; Poisson potential; Feynman–Kac formula; Principle eigenvalue (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.07.012

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