Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation
type: Item
instance of: scholarly article
title: Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation
zbMATH Open document ID: 0642.60038
DOI: 10.1007/BF00275500
author: Masaru Iizuka
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: We consider a sequence of discrete-parameter stochastic processes defined by solutions of stochastic difference equations. A condition is given that this sequence converges weakly to a continuous-parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous-time approximations for discrete-time models in random environments.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4046802
zbMATH Keywords: population biology
zbMATH Keywords: solutions of stochastic difference equations
zbMATH Keywords: stationary Gaussian processes
zbMATH Keywords: discrete-time models in random environments
MaRDI profile type: Publication
Wikidata QID: Q52428690
cites work: Q5560061
cites work: Q5848416
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description: scientific article; zbMATH DE number 4046802