Journal of Applied Probability

Automated state-dependent importance sampling for Markov jump processes via sampling from the zero-variance distribution

Adam W. Grace, Dirk P. Kroese, and Werner Sandmann

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Abstract

Many complex systems can be modeled via Markov jump processes. Applications include chemical reactions, population dynamics, and telecommunication networks. Rare-event estimation for such models can be difficult and is often computationally expensive, because typically many (or very long) paths of the Markov jump process need to be simulated in order to observe the rare event. We present a state-dependent importance sampling approach to this problem that is adaptive and uses Markov chain Monte Carlo to sample from the zero-variance importance sampling distribution. The method is applicable to a wide range of Markov jump processes and achieves high accuracy, while requiring only a small sample to obtain the importance parameters. We demonstrate its efficiency through benchmark examples in queueing theory and stochastic chemical kinetics.

Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 741-755.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932671

Digital Object Identifier
doi:10.1239/jap/1409932671

Mathematical Reviews number (MathSciNet)
MR3256224

Zentralblatt MATH identifier
1305.60081

Subjects
Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Secondary: 62M05: Markov processes: estimation

Keywords
Importance sampling adaptive automated improved cross entropy state dependent zero-variance distribution Markov jump process continuous-time Markov chain stochastic chemical kinetics queueing system

Citation

Grace, Adam W.; Kroese, Dirk P.; Sandmann, Werner. Automated state-dependent importance sampling for Markov jump processes via sampling from the zero-variance distribution. J. Appl. Probab. 51 (2014), no. 3, 741--755. doi:10.1239/jap/1409932671. https://projecteuclid.org/euclid.jap/1409932671


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