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.

引用

页数：4

共 50 条

[21] Efficient stochastic simulation of piecewise-deterministic Markov processes and its application to the Morris-Lecar model of neural dynamics
Pikovsky, Arkady
BIOLOGICAL CYBERNETICS, 2025, 119 (01)
[22] Qualitative properties of certain piecewise deterministic Markov processes
Benaim, Michel
Le Borgne, Stephane
Malrieu, Florent
Zitt, Pierre-Andre
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2015, 51 (03): : 1040 - 1075
[23] Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes
Pakdaman, Khashayar
Thieullen, Michele
Wainrib, Gilles
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (06) : 2292 - 2318
[24] A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions
Azais, Romain
Genadot, Alexandre
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2018, 47 (08) : 1812 - 1829
[25] Stochastic modelling and prediction of fatigue crack propagation using piecewise-deterministic Markov processes
Ben Abdessalem, Anis
Azais, Romain
Touzet-Cortina, Marie
Gegout-Petit, Anne
Puiggali, Monique
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY, 2016, 230 (04) : 405 - 416
[26] Non-Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise-Deterministic Markov Processes
Azais, Romain
Dufour, Francois
Gegout-Petit, Anne
SCANDINAVIAN JOURNAL OF STATISTICS, 2014, 41 (04) : 950 - 969
[27] Optimal choice among a class of nonparametric estimators of the jump rate for piecewise-deterministic Markov processes
Azais, Romain
Muller-Gueudin, Aurelie
ELECTRONIC JOURNAL OF STATISTICS, 2016, 10 (02): : 3648 - 3692
[28] PIECEWISE-DETERMINISTIC MARKOV-PROCESSES - A GENERAL-CLASS OF NON-DIFFUSION STOCHASTIC-MODELS
DAVIS, MHA
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1984, 46 (03): : 353 - 388
[29] STRONG LAW OF LARGE NUMBERS FOR HARMONIZABLE PROCESSES
ROUSSEAUEGELE, J
ANNALES DE L INSTITUT HENRI POINCARE SECTION B-CALCUL DES PROBABILITES ET STATISTIQUE, 1979, 15 (02): : 175 - 186
[30] The strong law of large numbers for random processes
Naumov A.A.
Moscow University Computational Mathematics and Cybernetics, 2010, 34 (1) : 31 - 36

← 1 2 3 4 5 →