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A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…

Probability · Mathematics 2020-12-07 Dawid Czapla , Katarzyna Horbacz , Hanna Wojewódka-Ściążko

We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…

Probability · Mathematics 2020-12-04 Dawid Czapla , Sander C. Hille , Katarzyna Horbacz , Hanna Wojewódka-Ściążko

In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…

Optimization and Control · Mathematics 2023-11-16 Xin Guo , Aiko Kurushima , Alexey Piunovskiy , Yi Zhang

For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…

Dynamical Systems · Mathematics 2018-04-05 Michel Benaïm , Fritz Colonius , Lettau Ralph

We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…

Probability · Mathematics 2024-03-26 Dawid Czapla , Katarzyna Horbacz , Hanna Wojewódka-Ściążko

A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…

Statistics Theory · Mathematics 2016-05-24 Romain Azaïs , Aurélie Muller-Gueudin

This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying…

Probability · Mathematics 2007-05-23 Xianping Guo , Ulrich Rieder

Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…

Probability · Mathematics 2022-09-30 Andrea Bertazzi , Joris Bierkens , Paul Dobson

For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of…

Probability · Mathematics 2025-11-13 Nicolas Champagnat , Edouard Strickler , Denis Villemonais

We consider Piecewise Deterministic Markov Processes (PDMPs) with a finite set of discrete states. In the regime of fast jumps between discrete states, we prove a law of large number and a large deviation principle. In the regime of fast…

Probability · Mathematics 2008-09-16 A. Faggionato , D. Gabrielli , M. Ribezzi Crivellari

Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…

Analysis of PDEs · Mathematics 2009-04-10 W. Wang , A. J. Roberts

Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…

Computation · Statistics 2019-06-03 Alexander Terenin , Daniel Thorngren

We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…

Optimization and Control · Mathematics 2017-11-22 Xin Guo , Yi Zhang

This article considers the average optimality for a continuous-time Markov decision process with Borel state and action spaces and an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is…

Optimization and Control · Mathematics 2014-03-05 Yi Zhang

Piecewise deterministic Markov processes (PDMPs) are a class of continuous-time Markov processes that were recently used to develop a new class of Markov chain Monte Carlo algorithms. However, the implementation of the processes is…

Computation · Statistics 2024-08-08 Charly Andral , Kengo Kamatani

An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding…

Numerical Analysis · Mathematics 2025-10-20 Mario Annunziato

In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…

Probability · Mathematics 2023-10-06 Dawid Czapla , Sander C. Hille , Katarzyna Horbacz , Hanna Wojewódka-Ściążko

We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…

Probability · Mathematics 2018-11-20 Aline Marguet

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…

Probability · Mathematics 2013-05-28 Adrien Brandejsky , Benoîte de Saporta , François Dufour

This paper deals with the general discounted impulse control problem of a piecewise deterministic Markov process. We investigate a new family of epsilon-optimal strategies. The construction of such strategies is explicit and only…

Probability · Mathematics 2016-03-28 Benoîte de Saporta , François Dufour , Alizée Geeraert