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Sample path moderate deviations for non-stationary power-law shot noise processes

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  28 March 2025

Ran Wang ,
Yimin Xiao  and
Qingshan Yang
Ran Wang*
Affiliation:
Wuhan University
Yimin Xiao*
Affiliation:
Michigan State University
Qingshan Yang*
Affiliation:
Northeast Normal University
*
*Postal address: School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China. Email: [email protected]
**Postal address: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA. Email: [email protected]
***Postal address: KLAS, Key Laboratory of Big Data Analysis of Jilin Province, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China. Corresponding author email: [email protected]
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Abstract

We establish a sample path moderate deviation principle for the integrated shot noise process with Poisson arrivals and non-stationary noises. As in Pang and Taqqu (2019), we assume that the noise is conditionally independent given the arrival times, and the distribution of each noise depends on its arrival time. As applications, we derive moderate deviation principles for the workload process and the running maximum process for a stochastic fluid queue with the integrated shot noise process as the input; we also show that a steady-state distribution exists and derive the exact tail asymptotics.

Keywords

Moderate deviationsPoisson shot noisegeneralized fractional Brownian motion

MSC classification

Primary: 60F10: Large deviations
Secondary: 60F17: Functional limit theorems; invariance principles 60G55: Point processes
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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