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Related papers: Piecewise Deterministic Markov Processes and their…

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We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…

Probability · Mathematics 2015-12-08 Ryszard Rudnicki , Marta Tyran-Kaminska

In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…

Probability · Mathematics 2014-12-24 Florent Malrieu

We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate.…

Probability · Mathematics 2014-04-08 Michel Benaïm , Stéphane Le Borgne , Florent Malrieu , Pierre-André Zitt

We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to…

Machine Learning · Statistics 2024-11-06 Andrea Bertazzi , Dario Shariatian , Umut Simsekli , Eric Moulines , Alain Durmus

We consider a piecewise-deterministic Markov process (PDMP) with general conditional distribution of inter-occurrence time, which is called a general PDMP here. Our purpose is to establish the theory of measure-valued generator for general…

Probability · Mathematics 2017-04-27 Zhaoyang Liu , Yong Jiao , Guoxin Liu

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

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

Computation · Statistics 2024-09-09 Adrien Corenflos , Matthew Sutton , Nicolas Chopin

Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…

Machine Learning · Statistics 2024-06-28 Paul Fearnhead , Sebastiano Grazzi , Chris Nemeth , Gareth O. Roberts

In this paper, we consider a piecewise deterministic Markov process (PDMP), with known flow and deterministic transition measure, and unknown jump rate $\lambda$. To estimate nonparametrically the jump rate, we first construct an adaptive…

Statistics Theory · Mathematics 2020-12-09 Nathalie Krell , Emeline Schmisser

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…

Optimization and Control · Mathematics 2022-08-30 Eugene A. Feinberg , Pavlo O. Kasyanov , Michael Z. Zgurovsky

We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $\beta_m$ (if the sampled parts are…

Probability · Mathematics 2007-05-23 Eddy Mayer-Wolf , Ofer Zeitouni , Martin P. W. Zerner

We propose to model the records of the maximum Drawdown in capital markets by means a Piecewise Deterministic Markov Process (PDMP). We derive statistical results such as the mean and variance that describes the sequence of maximum Drawdown…

Risk Management · Quantitative Finance 2025-04-01 Rolando Rubilar-Torrealba , Lisandro Fermin , Soledad Torres

We develop a general framework for piecewise deterministic Markov process (PDMP) samplers that enables efficient Bayesian inference in non-linear inverse problems with expensive likelihoods. The key ingredient is a surrogate-assisted…

Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…

Methodology · Statistics 2017-05-03 Romain Azaïs , Alexandre Genadot

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…

Dynamical Systems · Mathematics 2014-08-04 Xavier Garcia , Jennifer Kunze , Thomas Rudelius , Anthony Sanchez , Sijing Shao , Emily Speranza , Chad Vidden

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control…

Probability · Mathematics 2008-09-03 O. L. V. Costa , F. Dufour

This paper introduces Switching Processes, called SP. Their constructions are inspired by the PDMP's ones (PDMP stands for Piecewise Deterministic Markov Process). A Markov process, called the intrinsic process, replaces the PDMP's flow.…

Probability · Mathematics 2017-01-19 Christiane Cocozza-Thivent

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only…

Computation · Statistics 2023-09-07 Ajay Jasra , Kengo Kamatani , Mohamed Maama

In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…

Probability · Mathematics 2021-06-09 Branda Goncalves , Thierry Huillet , Eva Löcherbach

Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific and engineering disciplines. Two key frameworks that have emerged for modeling and solving control…

Methodology · Statistics 2025-04-15 Alice Cleynen , Benoîte de Saporta , Orlane Rossini , Régis Sabbadin , Amélie Vernay