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) |
|---|---|
| Article number | 7039916 |
| Pages (from-to) | 3401-3407 |
| Number of pages | 7 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 2015-February |
| Issue number | February |
| DOIs | |
| State | Published - Jan 1 2014 |
| Event | 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014 |
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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 journal › Conference article
}
TY - JOUR
T1 - Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation
AU - Maginnis, Peter A.
AU - West, Matthew
AU - Dullerud, Geir E.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84988227664&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84988227664&partnerID=8YFLogxK
U2 - 10.1109/CDC.2014.7039916
DO - 10.1109/CDC.2014.7039916
M3 - Conference article
AN - SCOPUS:84988227664
VL - 2015-February
SP - 3401
EP - 3407
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
IS - February
M1 - 7039916
ER -