Approximations: replacing random variables with their means. (December 2014)

• Record Type: Journal Article
• Authors: Gani, Joe
• Is Part Of: Journal of applied probability. Volume 51:Number A(2014)
• Page Start: 57
• Page End: 62
• Publication Date: 2014-12
• Subjects: Markov chain, -- random variable, -- mean, -- approximation; 60J10, -- 60G07; 519.2
• DOI: 10.1239/jap/1417528466
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : One of the standard methods for approximating a bivariate continuous-time Markov chain { X ( t ), Y ( t ): t ≥ 0}, which proves too difficult to solve in its original form, is to replace one of its variables by its mean, This leads to a simplified stochastic process for the remaining variable which can usually be solved, although the technique is not always optimal. In this note we consider two cases where the method is successful for carrier infections and mutating bacteria, and one case where it is somewhat less so for the SIS epidemics.