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Approximate Analysis of Biological Systems by Hybrid Switching Jump Diffusion by Angius, Alessio; Balbo, Gianfranco; Beccuti, Marco; Bibbona, Enrico; Horvath, Andras; Sirovich, Roberta is a scholarly article available to read on EtoBox.

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In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations, while the other uses a diffusion process. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior. In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation, namely when the process reaches the boundary with non-negligible probability. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the ju

Author

Angius, Alessio; Balbo, Gianfranco; Beccuti, Marco; Bibbona, Enrico; Horvath, Andras; Sirovich, Roberta

Published

2014

Language

EN