# Gaussian Ornstein-Uhlenbeck and Bogoliubov processes: Asymptotics of small deviations for L p -functionals, 0 < p < ∞

Gaussian Ornstein-Uhlenbeck and Bogoliubov processes: Asymptotics of small deviations for L p... We prove results on sharp asymptotics of probabilities $$P\left\{ {\int\limits_0^1 {\left| {X(t)} \right|^p dt < \varepsilon ^p } } \right\}, \varepsilon \to 0,$$ where 0 < p < ∞, for three Gaussian processes X(t), namely the stationary and nonstationary Ornstein-Uhlenbeck process and the Bogoliubov process. The analysis is based on the Laplace method for sojourn times of a Wiener process. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Gaussian Ornstein-Uhlenbeck and Bogoliubov processes: Asymptotics of small deviations for L p -functionals, 0 < p < ∞

, Volume 50 (4) – Jan 7, 2015
19 pages

/lp/springer_journal/gaussian-ornstein-uhlenbeck-and-bogoliubov-processes-asymptotics-of-3wgKPqeHeU
Publisher
Springer Journals
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946014040073
Publisher site
See Article on Publisher Site

### Abstract

We prove results on sharp asymptotics of probabilities $$P\left\{ {\int\limits_0^1 {\left| {X(t)} \right|^p dt < \varepsilon ^p } } \right\}, \varepsilon \to 0,$$ where 0 < p < ∞, for three Gaussian processes X(t), namely the stationary and nonstationary Ornstein-Uhlenbeck process and the Bogoliubov process. The analysis is based on the Laplace method for sojourn times of a Wiener process.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 7, 2015

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