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Abstract
Continuous time Markov chain (CTMC) and It 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.
Mathematics Subject Classification:
Financial support was provided by the Texas Advanced Research Program 003644-0001-2006 and by the National Science Foundation DMS-0718302.