ABSTRACT
Jump diffusion processes represents an extension of the piecewise deterministic processes. Informally, the deterministic flows between the jumps of the piecewise deterministic process are replaced by the diffusion processes introduced. This chapter discusses the Doeblin-Ito differential calculus for these processes and use it to derive the Fokker-Planck equation. Further on, it introduces jump diffusion processes with killing in terms of Feynman-Kac semigroups. The chapter shows in some details the usefulness of these models for solving some classes of partial differential equations. It has chosen to present these continuous time stochastic processes from the practitioner's point of view, using simple arguments based on their discrete approximations. Jump diffusion processes represent the most general class of Markovian stochastic processes encountered in practice. It has chosen to present these continuous time stochastic processes from the practitioner's point of view, using simple arguments based on their discrete approximations.
