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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…

Optimization and Control · Mathematics 2017-09-28 Alice Cleynen , Benoîte de Saporta

A distributional equation as a criterion for invariant measures of Markov processes associated to L\'evy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated…

Probability · Mathematics 2022-08-17 Anita Behme , David Oechsler

Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time.…

Systems and Control · Electrical Eng. & Systems 2025-05-16 Spencer Schutz , Charlott Vallon , Ben Recht , Francesco Borrelli

This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…

Probability · Mathematics 2014-07-04 Eugene A. Feinberg , Pavlo O. Kasyanov , Michael Z. Zgurovsky

We revisit closed-loop performance guarantees for Model Predictive Control in the deterministic and stochastic cases, which extend to novel performance results applicable to receding horizon control of Partially Observable Markov Decision…

Optimization and Control · Mathematics 2020-05-01 Martin A. Sehr , Robert R. Bitmead

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

We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…

Probability · Mathematics 2017-04-03 Tristan Benoist , Martin Fraas , Yan Pautrat , Clément Pellegrini

We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions.…

Analysis of PDEs · Mathematics 2015-06-17 Nathan Glatt-Holtz , Igor Kukavica , Vlad Vicol , Mohammed Ziane

We present a numerical method to compute expectations of functionals of a piecewise-deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the…

Probability · Mathematics 2012-01-31 Adrien Brandejsky , Benoîte de Saporta , François Dufour

The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…

Dynamical Systems · Mathematics 2019-01-03 Tobias Hurth , Christian Kuehn

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

Methodology · Statistics 2018-05-16 Paul Vanetti , Alexandre Bouchard-Côté , George Deligiannidis , Arnaud Doucet

We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The…

Probability · Mathematics 2017-07-14 Chang-Han Rhee , Peter Glynn

Piecewise-deterministic Markov processes (PDMPs) are often used to model abrupt changes in the global environment or capabilities of a controlled system. This is typically done by considering a set of "operating modes" (each with its own…

Optimization and Control · Mathematics 2025-02-13 Marissa Gee , Alexander Vladimirsky

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

Markov Decision Processes (Mdps) form a versatile framework used to model a wide range of optimization problems. The Mdp model consists of sets of states, actions, time steps, rewards, and probability transitions. When in a given state and…

Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…

Rings and Algebras · Mathematics 2023-01-02 Chengshen Xu

We consider the synthesis of control policies for probabilistic systems, modeled by Markov decision processes, operating in partially known environments with temporal logic specifications. The environment is modeled by a set of Markov…

Logic in Computer Science · Computer Science 2012-03-07 Tichakorn Wongpiromsarn , Emilio Frazzoli

In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the…

Optimization and Control · Mathematics 2023-02-27 Elliot Cartee , Antonio Farah , April Nellis , Jacob van Hook , Alexander Vladimirsky

This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying…

Probability · Mathematics 2011-08-31 Benoîte de Saporta , François Dufour

We construct the non-linear Markov process connected with biological model of bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory.

Probability · Mathematics 2015-06-22 Arseniy V. Akopyan , Sergey A. Pirogov , Aleksandr N. Rybko