Approximations of Piecewise Deterministic Markov Processes and their convergence properties

Understand

Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods.

• A PDMP is specified by three characteristic quantities: the deterministic motion, the law of the random event times, and the jump kernels.
• The applicability of PDMPs to real world scenarios is currently limited by the fact that these processes can be simulated only when these three characteristics of the process can be simulated exactly.
• In order to overcome this problem, we introduce discretisation schemes for PDMPs which make their approximate simulation possible.