Weighted \(L^{p}\)-norms, \(p\geq 2\), for a Wiener process: exact asymptotics of small deviations

DOI10.3103/S0027132215020035zbMath1322.60033OpenAlexW1134375365MaRDI QIDQ2354941

V. R. Fatalov

Publication date: 27 July 2015

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132215020035

zbMATH Keywords

Wiener processstochastic integralssmall deviation probabilities\(L^{p}\)-norms

Mathematics Subject Classification ID

Large deviations (60F10) Stochastic integrals (60H05) Limit theorems in probability theory (60F99)

Cites Work

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• Small deviations for two classes of Gaussian stationary processes and \(L^p\)-functionals, \(0<p\leq\infty\)
• Small ball probabilities for Gaussian Markov processes under the \(L_p\)-norm.
• Exact small ball asymptotics in weighted \(L_2\)-norm for some Gaussian processes
• Lectures on Gaussian Processes
• Approximation and entropy numbers of Volterra operators with application to Brownian motion
• Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields
• 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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