ABSTRACT
This chapter is concerned with calculating distributions of the process and the expectations of functionals of it. It devotes to introducing various transformations of Piecewise-Deterministic Processes (PDPs) with the help of which such connections can be recognized. The chapter shows that is the unique solution of a set of integro-differential equations. It introduces a general recursive method by which numerical solutions may be obtained. The chapter considres the important topic of stationary distributions. It explores the connection between the expectations of certain functionals of a PDP and systems of integro-differential equations associated with its generator. The chapter examines a recursive scheme which provides the basis for a widely applicable numerical technique for computing discounted or finite-horizon costs. It develops material originally presented in M. H. A. Davis. There are strong analogies with stochastic calculus based on Brownian motion.
