Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation

Peter A. Maginnis; Matthew West; Geir E. Dullerud

doi:10.1109/CDC.2014.7039916

Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation

Peter A. Maginnis
, Matthew West
, Geir E. Dullerud

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

We provide an exact, continuous time extension to previous work in anticorrelated stochastic process simulation that was performed in an approximate, discrete time setting. These methods reduce the variance of continuous time Monte Carlo for Markov jump process systems. We rigorously construct antithetic Poisson processes and analytically prove the negative correlation between pairs. We then show how these anticorrelated Poisson processes can be used to drive Markov jump processes via a random time change representation. Finally, we provide a sufficient condition for variance reduction in the jump process context as well as demonstrate a simple example.

Original language	English (US)
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3401-3407
Number of pages	7
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7039916
State	Published - 2014
Externally published	Yes
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	12/15/14 → 12/17/14

Bibliographical note

Publisher Copyright:
© 2014 IEEE.

Publisher link

10.1109/CDC.2014.7039916

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Maginnis, P. A., West, M., & Dullerud, G. E. (2014). Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 3401-3407). Article 7039916 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039916

Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation. / Maginnis, Peter A.; West, Matthew; Dullerud, Geir E.
53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 3401-3407 7039916 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Maginnis, PA, West, M & Dullerud, GE 2014, Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7039916, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 3401-3407, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 12/15/14. https://doi.org/10.1109/CDC.2014.7039916

Maginnis PA, West M, Dullerud GE. Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation. In 53rd IEEE Conference on Decision and Control,CDC 2014. February ed. Institute of Electrical and Electronics Engineers Inc. 2014. p. 3401-3407. 7039916. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7039916

Maginnis, Peter A. ; West, Matthew ; Dullerud, Geir E. / Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation. 53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 3401-3407 (Proceedings of the IEEE Conference on Decision and Control; February).

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Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation

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