ABSTRACT
This chapter introduces a general class of processes called piecewise-deterministic Markov processes (PDPs) which are stochastic models having precisely this property, and sufficiently general to cover a wide variety of applied problems as special cases. Constructing the PDP model corresponding to a particular application proceeds by way of one or both of two well-known principles: the inclusion of supplementary variables to turn an initially non-Markov process into a Markov process, and the use of indicator variables to keep track of the various possible 'configurations' of the system under study. A PDP consists of a mixture of deterministic motion and random jumps. The chapter provides some information about deterministic differential equations and vector fields, and about methods for constructing random variables with specified distributions. It devotes to establishing the main properties of PDPs in their capacity as Markov processes, namely the strong Markov property, an exact characterization of the extended generator, and the fact that PDPs are right processes.
