Functional limit theorems for a new class of non-stationary shot noise processes

Guodong Pang, Yuhang Zhou

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study a class of non-stationary shot noise processes which have a general arrival process of noises with non-stationary arrival rate and a general shot shape function. Given the arrival times, the shot noises are conditionally independent and each shot noise has a general (multivariate) cumulative distribution function (c.d.f.) depending on its arrival time. We prove a functional weak law of large numbers and a functional central limit theorem for this new class of non-stationary shot noise processes in an asymptotic regime with a high intensity of shot noises, under some mild regularity conditions on the shot shape function and the conditional (multivariate) c.d.f. We discuss the applications to a simple multiplicative model (which includes a class of non-stationary compound processes and applies to insurance risk theory and physics) and the queueing and work-input processes in an associated non-stationary infinite-server queueing system. To prove the weak convergence, we show new maximal inequalities and a new criterion of existence of a stochastic process in the space D given its consistent finite dimensional distributions, which involve a finite set function with the superadditive property.

Original languageEnglish (US)
Pages (from-to)505-544
Number of pages40
JournalStochastic Processes and their Applications
Volume128
Issue number2
DOIs
StatePublished - Feb 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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