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Asymptotic behavior of the weak approximation to a class of Gaussian processes

Part of: Probability theory on algebraic and topological structures Limit theorems

Published online by Cambridge University Press:  16 September 2021

Hui Jiang  and
Qingshan Yang
Hui Jiang*
Affiliation:
Nanjing University of Aeronautics and Astronautics
Qingshan Yang*
Affiliation:
Northeast Normal University
*
*Postal address: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China
**Postal address: School of Mathematics and Statistics, Northeast Normal University, Changchun, P.R. China. Email: [email protected]
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Abstract

We study, under mild conditions, the weak approximation constructed from a standard Poisson process for a class of Gaussian processes, and establish its sample path moderate deviations. The techniques consist of a good asymptotic exponential approximation in moderate deviations, the Besov–Lèvy modulus embedding, and an exponential martingale technique. Moreover, our results are applied to the weak approximations associated with the moving average of Brownian motion, fractional Brownian motion, and an Ornstein–Uhlenbeck process.

Keywords

Exponential martingaleGaussian processmoderate deviationsPoisson processweak approximation

MSC classification

Primary: 60F10: Large deviations
Secondary: 60F17: Functional limit theorems; invariance principles 60B10: Convergence of probability measures
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 3 , September 2021 , pp. 693 - 707
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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