On binomial observation of continuous-time Markovian population models

Title: On binomial observation of continuous-time Markovian population models
Creator: Bean, N. G.; Elliott, R.; Eshragh, A.; Ross, J. V.
Relation: ARC.DP110101929 & ARC.DP08677639
Relation: Journal of Applied Probability Vol. 52, Issue 2, p. 457-472
Publisher Link: http://dx.doi.org/10.1017/S0021900200012572
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2015
Description: In this paper we consider a class of stochastic processes based on binomial observations of continuous-time, Markovian population models. We derive the conditional probability mass function of the next binomial observation given a set of binomial observations. For this purpose, we first find the conditional probability mass function of the underlying continuous-time Markovian population model, given a set of binomial observations, by exploiting a conditional Bayes' theorem from filtering, and then use the law of total probability to find the former. This result paves the way for further study of the stochastic process introduced by the binomial observations. We utilize our results to show that binomial observations of the simple birth process are non-Markovian.
Subject: continuous-time Markovian population model; binomial observation; simple birth process; filtering
Identifier: http://hdl.handle.net/1959.13/1332864
Identifier: uon:26955
Identifier: ISSN:1475-6072
Language: eng
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