Analysis of Timed Properties Using the Jump-Diffusion Approximation

Paolo Ballarini (1) , Marco Beccuti (2) , Enrico Bibbona , Andras Horvath (3) , Roberta Sirovich (4) , Jeremy Sproston (5)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 UPO - Università degli Studi del Piemonte Orientale - Amedeo Avogadro
3 Dipartimento di Informatica [Torino]
4 Neurosciences précliniques
5 UNITO - Università degli studi di Torino = University of Turin

Density dependent Markov chains (DDMCs) describe the interaction of groups of identical objects. In case of large numbers of objects a DDMC can be approximated efficiently by means of either a set of ordinary differential equations (ODEs) or by a set of stochastic differential equations (SDEs). While with the ODE approximation the chain stochasticity is not maintained, the SDE approximation, also known as the diffusion approximation, can capture specific stochastic phenomena (e.g., bi-modality) and has also better convergence characteristics. In this paper we introduce a method for assessing temporal properties, specified in terms of a timed automaton, of a DDMC through a jump diffusion approximation. The added value is in terms of runtime: the costly simulation of a very large DDMC model can be replaced through much faster simulation of the corresponding jump diffusion model. We show the efficacy of the framework through the analysis of a biological oscillator.

Mots clés: diffusion approximation; stochastic differential equations with jumps; statistical model checking

Domaines: Théorie et langage formel [cs.FL]

Paolo Ballarini, Marco Beccuti, Enrico Bibbona, Andras Horvath, Roberta Sirovich, et al.. Analysis of Timed Properties Using the Jump-Diffusion Approximation. European Workshop on Performance Engineering, Sep 2017, Berlin, Germany. ⟨hal-01817472⟩