Qualitative properties of certain piecewise deterministic Markov processes
نویسندگان
چکیده
منابع مشابه
Qualitative properties of certain piecewise deterministic Markov processes
We study a class of Piecewise Deterministic Markov Processes with state space R d × 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. The jump rates may depend on the whole position of the process. Working under the general assumption that the process stays in a compact set, we detail a p...
متن کاملDemographic noise and piecewise deterministic Markov processes.
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from nonequilibrium statistical mechanics to study the influence that intrinsic noise has on the qualitative behavior of the system. We discuss the application of...
متن کاملPiecewise deterministic Markov processes in biological models
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 expression, physiologically structured populations, as well as neural activity. General results concerning asymptotic properties of stochastic semigroups induc...
متن کاملStochastic Equivalence of Cpdp-automata and Piecewise Deterministic Markov Processes
CPDP is a class of automata designed for compositional specification/analysis of certain stochastic hybrid processes. We prove equivalence of the stochastic behaviors of CPDPs (newly defined here) and PDPs. With this result we obtain a clear stochastic processes semantics for CPDPs and we obtain the opportunity to use the powerful PDP analysis techniques in the context of the compositional fram...
متن کاملNumerical method for optimal stopping of piecewise deterministic Markov processes
We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location – inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2015
ISSN: 0246-0203
DOI: 10.1214/14-aihp619