Comparison of markov chain and stochastic differential equation population models under higher-order moment closure approximations

Amy J. Ekanayake, LINDA J.S. ALLEN

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Continuous time Markov chain (CTMC) and Itô stochastic differential equation (SDE) models are derived for a population with births, immigration and deaths (BID model). Differential equations are derived for the moments of the distribution for each stochastic model. Each moment differential equation depends on higher-order moments. Assumptions are made regarding higher-order moments to form a finite, solvable system. Conditions are given under which the CTMC and SDE BID models have the same moment solution or the same stationary solution. The close agreement between the CTMC and SDE models is illustrated in three numerical examples based on normal or log-normal moment closure assumptions.

Original languageEnglish
Pages (from-to)907-927
Number of pages21
JournalStochastic Analysis and Applications
Volume28
Issue number6
DOIs
StatePublished - Nov 2010

Keywords

  • Itô
  • Kolmogorov differential equation
  • Markov chain
  • Metapopulation
  • Moment closure
  • Stochastic differential equation

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