Hybrid Semantics of Stochastic Programs with Dynamic Reconfiguration

TL;DR

This paper enhances the hybrid semantics of stochastic programs by enabling dynamic reconfiguration between discrete and continuous components, improving modeling flexibility for systems like biochemical processes.

Contribution

It introduces a flexible translation scheme that allows dynamic reconfiguration of the discrete and continuous aspects in hybrid semantics of stochastic programs.

Findings

Increased flexibility in hybrid semantics modeling.

Better approximation of stochastic program dynamics.

Connections with hybrid simulation strategies for biochemical systems.

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.