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: Contribution to journalConference article

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 languageEnglish (US)
Article number7039916
Pages (from-to)3401-3407
Number of pages7
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

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Exact Simulation
Markov Jump Processes
Poisson process
Random processes
Continuous Time
Random Time Change
Jump Process
Variance Reduction
Process Simulation
Stochastic Simulation
Stochastic Processes
Discrete-time
Sufficient Conditions
Demonstrate
Context

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation. / Maginnis, Peter A.; West, Matthew; Dullerud, Geir E.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7039916, 01.01.2014, p. 3401-3407.

Research output: Contribution to journalConference article

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