Some comments on approximations to the master equation

Moshe Gitterman, George H. Weiss

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

A common strategy for approximating a master equation is to replace it by a diffusion-like equation. Many methods for deriving the form of such an equation have been suggested in the literature. We compare two of these in the light of an example in which the master equation can be solved exactly. One of these is the van KampenΩ-expansion, which generally does not give a useful approximation to the equilibrium solution, and the second is a technique which preserves the noise-free dynamics and gives the correct equilibrium solution. It is shown that the second moment calculated in the latter approximation is not an accurate one at short times. The difficulty is the restriction of the approximating equation to the diffusion form.

Original languageEnglish
Pages (from-to)503-510
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Volume170
Issue number3
DOIs
StatePublished - 15 Jan 1991

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