An optimal finite state projection method

Vikram Sunkara; Markus Hegland

doi:10.1016/j.procs.2010.04.177

An optimal finite state projection method

Vikram Sunkara^*, Markus Hegland

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

It is well known that many realistic mathematical models of biological and chemical systems, such as enzyme cascades and gene regulatory networks, need to include stochasticity. These systems can be described as Markov processes and are modelled using the Chemical Master Equation (CME). The CME is a differential-difference equation (continuous in time and discrete in the state space) for the probability of certain state at a given time. The state space is the population count of species in the system. A successful method for computing the CME is the Finite State Projection Method (FSP). In this paper we will give the mathematical background of the FSP and propose a new addition to the FSP which guaranties our approximation to have optimal order.

Original language	English
Pages (from-to)	1579-1586
Number of pages	8
Journal	Procedia Computer Science
Volume	1
Issue number	1
DOIs	https://doi.org/10.1016/j.procs.2010.04.177
Publication status	Published - 2010

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AU - Sunkara, Vikram

AU - Hegland, Markus

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AB - It is well known that many realistic mathematical models of biological and chemical systems, such as enzyme cascades and gene regulatory networks, need to include stochasticity. These systems can be described as Markov processes and are modelled using the Chemical Master Equation (CME). The CME is a differential-difference equation (continuous in time and discrete in the state space) for the probability of certain state at a given time. The state space is the population count of species in the system. A successful method for computing the CME is the Finite State Projection Method (FSP). In this paper we will give the mathematical background of the FSP and propose a new addition to the FSP which guaranties our approximation to have optimal order.

KW - Chemical master equation

KW - Finite state projection

KW - State space growth

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JO - Procedia Computer Science

JF - Procedia Computer Science

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An optimal finite state projection method

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