Sample path moderate deviations for shot noise processes in the high intensity regime

Sumith Reddy Anugu and Guodong Pang

Stochastic Processes and their Applications, 2024, vol. 176, issue C

Abstract: We study the sample-path moderate deviation principle (MDP) for shot noise processes in the high intensity regime. The shot noise processes have a renewal arrival process, non-stationary noises (with arrival-time dependent distributions) and a general shot response function of the noises. The rate function in the MDP exhibits a memory phenomenon in this asymptotic regime, which is in contrast with that in the conventional time–space scaling regime. To prove the sample-path MDP, we first establish that this is equivalent to establishing the sample-path MDP of another process that is easier to study. We prove its finite-dimensional MDP and then establish the exponential tightness under the Skorohod J1 topology. This results in the sample-path MDP in D under the Skorohod J1 topology with a rate function that is derived from the rate function in the finite-dimensional MDP using the tools of reproducing kernel Hilbert space. In the proofs, because of the non-stationarity of shot noise process, we establish a new exponential maximal inequality and use it to prove exponential tightness and the aforementioned equivalence.

Keywords: Sample path moderate deviation principle; Shot noise process; Renewal arrival process; Non-stationary noise distribution (arrival-time dependent distributions) (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104432

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