Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein–Uhlenbeck Processes, $p>0$

V. R. Fatalov

Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 72-99

Résumé

The paper proves the results on exact asymptotics of the probabilities $\mathbf{P}_\mu\{T^{-1}\times\int_0^T|\eta_\gamma(t)|^p\,dt<d\}$, $T\to\infty$, for $p>0$ for Gaussian Markov Ornstein–Uhlenbeck processes $\eta_\gamma$ and also for their conditional versions. The author uses the Laplace method for the occupation time of Markov processes with continuous time. The calculations are given for the case $p=2$ with the help of the solution of the extremal problem for the action functional.

Détail

Keywords: large deviations, Gaussian processes, Markov processes, action functional, Ornstein–Uhlenbeck processes, Weber differential equation.

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