Analysis of Timed Properties Using the Jump-Diffusion Approximation - Archive ouverte HAL Access content directly
Conference Papers Year : 2017

Analysis of Timed Properties Using the Jump-Diffusion Approximation

Abstract

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.
Fichier principal
Vignette du fichier
main.pdf (624.18 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01817472 , version 1 (18-06-2018)

Identifiers

  • HAL Id : hal-01817472 , version 1

Cite

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⟩
84 View
157 Download

Share

Gmail Mastodon Facebook X LinkedIn More