The Strong Law of Large Numbers for Certain Piecewise-Deterministic Markov Processes with Application to a Gene Expression Model

被引：0
|
作者：
Czapla, Dawid [1 ]
Horbacz, Katarzyna [1 ]
Wojewodka, Hanna [1 ]
机构：
[1] Univ Silesia Katowice, Inst Math, Bankowa 14, PL-40007 Katowice, Poland
来源：
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017) | 2018年 / 1978卷
关键词：
D O I：
10.1063/1.5044078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main goal of this paper is to establish the strong law of large numbers (SLLN) for a subclass of piecewise-deterministic Markov processes (PDMPs). On the way to this result, we provide sufficient conditions for the existence of an exponentially attracting invariant distribution for the Markov chain given by the post-jump locations of a PDMP. Furthermore, we obtain a one-to-one correspondence between invariant measures of such a chain and invariant measures of the PDMP. Finally, we illustrate the applicability of our results for a model of prokaryotic gene expression.
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页数：4
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