Hybrid Semantics of Stochastic Programs with Dynamic Reconfiguration

Abstract

We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Deterministic Markov Process with a stochastic program. The specific contribution in this work consists in an increase of the flexibility of the translation scheme, obtained by allowing a dynamic reconfiguration of the degree of discreteness/continuity of the semantics. We also discuss the relationships of this approach with other hybrid simulation strategies for biochemical systems.