### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the 2012 Winter Simulation Conference |

Subtitle of host publication | Washington D.C. |

Editors | C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, A.M. Uhrmacher |

Publisher | IEEE |

Number of pages | 10 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- complexity theory
- networking
- multi-level Monte Carlo method
- computational efficiency

### Cite this

*Proceedings of the 2012 Winter Simulation Conference: Washington D.C.*IEEE. https://doi.org/10.1109/WSC.2012.6465219

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*Proceedings of the 2012 Winter Simulation Conference: Washington D.C..*IEEE. https://doi.org/10.1109/WSC.2012.6465219

**Computing mean first exit times for stochastic processes using multi-level Monte Carlo.** / Higham, Desmond; Roj, Mikolaj.

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

TY - GEN

T1 - Computing mean first exit times for stochastic processes using multi-level Monte Carlo

AU - Higham, Desmond

AU - Roj, Mikolaj

PY - 2012

Y1 - 2012

N2 - The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.

AB - The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.

KW - complexity theory

KW - networking

KW - multi-level Monte Carlo method

KW - computational efficiency

UR - http://www.scopus.com/inward/record.url?scp=84874694507&partnerID=8YFLogxK

U2 - 10.1109/WSC.2012.6465219

DO - 10.1109/WSC.2012.6465219

M3 - Conference contribution book

BT - Proceedings of the 2012 Winter Simulation Conference

A2 - Laroque, C.

A2 - Himmelspach, J.

A2 - Pasupathy, R.

A2 - Rose, O.

A2 - Uhrmacher, A.M.

PB - IEEE

ER -