The Law of the Iterated Logarithm for Random Dynamical System with Jumps and State-Dependent Jump Intensity-Reference-Cited by-同舟云学术

The Law of the Iterated Logarithm for Random Dynamical System with Jumps and State-Dependent Jump Intensity

Published:2021-08-30 Issue:0 Volume:0 Page:
ISSN:2391-4238
Container-title:Annales Mathematicae Silesianae
language:en
Short-container-title:

Author:

Kubieniec Joanna¹

Affiliation:

1. Institute of Mathematics , University of Silesia in Katowice , Bankowa 14, 40-007 Katowice , Poland

Abstract

Abstract In this paper our considerations are focused on some Markov chain associated with certain piecewise-deterministic Markov process with a state-dependent jump intensity for which the exponential ergodicity was obtained in [4]. Using the results from [3] we show that the law of iterated logarithm holds for such a model.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/amsil-2021-0011

Reference16 articles.

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2. [2] D. Czapla, K. Horbacz, and H. Wojewódka-Ściążko, Ergodic properties of some piecewise-deterministic Markov process with application to a gene expression modelling, Stochastic Process. Appl. 130 (2020), no. 5, 2851–2885.

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4. [4] D. Czapla and J. Kubieniec, Exponential ergodicity of some Markov dynamical systems with application to a Poisson-driven stochastic differential equation, Dyn. Syst. 34 (2019), no. 1, 130–156.

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