### Abstract

Original language | Undefined |
---|---|

Title of host publication | Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012 |

Place of Publication | Trondheim, Norway |

Publisher | NTNU University Press |

Pages | 36-38 |

Number of pages | 3 |

ISBN (Print) | not assigned |

Publication status | Published - Jun 2012 |

### Publication series

Name | |
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Publisher | NTNU University Press |

### Keywords

- METIS-287910
- IR-80763
- Large times
- EWI-22016
- Rewards
- Importance sampling
- Rare event simulation

### Cite this

*Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012*(pp. 36-38). Trondheim, Norway: NTNU University Press.

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*Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012.*NTNU University Press, Trondheim, Norway, pp. 36-38.

**Fast simulation for slow paths in Markov models.** / Reijsbergen, D.P.; de Boer, Pieter-Tjerk; Scheinhardt, Willem R.W.; Haverkort, Boudewijn R.H.M.

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

TY - GEN

T1 - Fast simulation for slow paths in Markov models

AU - Reijsbergen, D.P.

AU - de Boer, Pieter-Tjerk

AU - Scheinhardt, Willem R.W.

AU - Haverkort, Boudewijn R.H.M.

PY - 2012/6

Y1 - 2012/6

N2 - Inspired by applications in the context of stochastic model checking, we are interested in using simulation for estimating the probability of reaching a specific state in a Markov chain after a large amount of time tau has passed. Since this is a rare event, we apply importance sampling. We derive approximate expressions for the sojourn times on a given path in a Markov chain conditional on the sum exceeding tau, and use those expressions to construct a change of measure. Numerical examples show that this change of measure performs very well, leading to high precision estimates in short simulation times.

AB - Inspired by applications in the context of stochastic model checking, we are interested in using simulation for estimating the probability of reaching a specific state in a Markov chain after a large amount of time tau has passed. Since this is a rare event, we apply importance sampling. We derive approximate expressions for the sojourn times on a given path in a Markov chain conditional on the sum exceeding tau, and use those expressions to construct a change of measure. Numerical examples show that this change of measure performs very well, leading to high precision estimates in short simulation times.

KW - METIS-287910

KW - IR-80763

KW - Large times

KW - EWI-22016

KW - Rewards

KW - Importance sampling

KW - Rare event simulation

M3 - Conference contribution

SN - not assigned

SP - 36

EP - 38

BT - Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012

PB - NTNU University Press

CY - Trondheim, Norway

ER -