Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein--Uhlenbeck Processes, $p>0$
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 72-99
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The paper proves the results on exact asymptotics of the probabilities $\mathbf{P}_\mu\{T^{-1}\times\int_0^T|\eta_\gamma(t)|^p\,dt$, $T\to\infty$, 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.
Keywords:
large deviations, Gaussian processes, Markov processes, action functional, Ornstein–Uhlenbeck processes, Weber differential equation.
@article{TVP_2008_53_1_a4,
author = {V. R. Fatalov},
title = {Occupation {Time} and {Exact} {Asymptotics} of {Distributions} of $L^p${-Functionals} of the {Ornstein--Uhlenbeck} {Processes,} $p>0$},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {72--99},
publisher = {mathdoc},
volume = {53},
number = {1},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a4/}
}
TY - JOUR AU - V. R. Fatalov TI - Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein--Uhlenbeck Processes, $p>0$ JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2008 SP - 72 EP - 99 VL - 53 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a4/ LA - ru ID - TVP_2008_53_1_a4 ER -
%0 Journal Article %A V. R. Fatalov %T Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein--Uhlenbeck Processes, $p>0$ %J Teoriâ veroâtnostej i ee primeneniâ %D 2008 %P 72-99 %V 53 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a4/ %G ru %F TVP_2008_53_1_a4
V. R. Fatalov. Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein--Uhlenbeck Processes, $p>0$. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 72-99. http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a4/