Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/101388
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Type: Journal article
Title: On binomial observations of continuous-time Markovian population models
Author: Bean, N.
Elliott, R.
Eshragh, A.
Ross, J.
Citation: Journal of Applied Probability, 2015; 52(2):457-472
Publisher: Applied Probability Trust
Issue Date: 2015
ISSN: 0021-9002
1475-6072
Statement of
Responsibility: 
N. G. Bean, R. Elliott, A. Eshragh, and J. V. Ross
Abstract: 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.
Keywords: Continuous-time Markovian population model; binomial observation; simple birth process; filtering
Rights: © Applied Probability Trust 2015
RMID: 0030033109
DOI: 10.1239/jap/1437658609
Grant ID: http://purl.org/au-research/grants/arc/DP110101929
http://purl.org/au-research/grants/arc/DP08677639
Appears in Collections:Mathematical Sciences publications

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