Journal of Applied Probability

On binomial observations of continuous-time Markovian population models

N. G. Bean, R. Elliott, A. Eshragh, and J. V. Ross

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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.

Article information

Source
J. Appl. Probab. Volume 52, Number 2 (2015), 457-472.

Dates
First available in Project Euclid: 23 July 2015

Permanent link to this document
http://projecteuclid.org/euclid.jap/1437658609

Digital Object Identifier
doi:10.1239/jap/1437658609

Mathematical Reviews number (MathSciNet)
MR3372086

Zentralblatt MATH identifier
1323.60101

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 62M09: Non-Markovian processes: estimation 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Continuous-time Markovian population model binomial observation simple birth process filtering

Citation

Bean, N. G.; Elliott, R.; Eshragh, A.; Ross, J. V. On binomial observations of continuous-time Markovian population models. J. Appl. Probab. 52 (2015), no. 2, 457--472. doi:10.1239/jap/1437658609. http://projecteuclid.org/euclid.jap/1437658609.


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