Gaussian Ornstein-Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for \( L^{p}\)-functionals, \(0

DOI10.1134/S0032946014040073zbMath1321.60068MaRDI QIDQ2352639

V. R. Fatalov

Publication date: 3 July 2015

Published in: Problems of Information Transmission (Search for Journal in Brave)

zbMATH Keywords

Gaussian processesOrnstein-Uhlenbeck processsmall deviationsBogoliubov process

Mathematics Subject Classification ID

Gaussian processes (60G15) Diffusion processes (60J60) Large deviations (60F10) Limit theorems in probability theory (60F99)

Related Items (2)

Integrals of Bessel processes and multi-dimensional Ornstein-Uhlenbeck processes: exact asymptotics for $ L^p$-functionals ⋮ Functional integrals for the Bogoliubov Gaussian measure: exact asymptotic forms

Cites Work

• Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure
• Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the \(L^{p}\) norm, \(2 \leq p \leq \infty\)
• Small deviations for two classes of Gaussian stationary processes and \(L^p\)-functionals, \(0<p\leq\infty\)
• Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm
• Exact asymptotics of large deviations of stationary Ornstein-Uhlenbeck processes for \(L^p\)-functionals, \(p>0\)
• Negative-order moments for $ L^p$-functionals of Wiener processes: exact asymptotics
• Exact asymptotics of Laplace-type Wiener integrals for $ L^p$-functionals
• Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein–Uhlenbeck Processes, $p>0$
• Some familiar examples for which the large deviation principle does not hold
• Exact asymptotics of small deviations for a stationary Ornstein-Uhlenbeck process and some Gaussian diffusion processes in the L p -norm, 2 ≤ p ≤ ∞
• Exact Small Deviation Asymptotics for Some Brownian Functionals
• The Laplace method for small deviations of Gaussian processes of Wiener type
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