Related papers: Piecewise deterministic Markov processes driven by…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
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.…
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…
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…
This paper introduces a novel stochastic framework for modelling tax evasion dynamics by extending the deterministic model of Bertotti and Modanese (2018) through the use of Piecewise Deterministic Markov Processes (PDMPs). A key limitation…
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…
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…
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…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
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…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
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…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Designing efficient and rigorous numerical methods for sequential decision-making under uncertainty is a difficult problem that arises in many applications frameworks. In this paper we focus on the numerical solution of a subclass of…
Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from the sound produced by a violin to the screeching of chalk…
In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions $\pi$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain…
We aim at characterizing the asymptotic behavior of value functions in the control of piece-wise deterministic Markov processes (PDMP) of switch type under nonexpansive assumptions. For a particular class of processes inspired by temperate…