Splitting for rare event simulation: A large deviation approach to design and analysis

Thomas Dean and Paul Dupuis

Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 562-587

Abstract: Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set B before another set A, and it is assumed that this probability satisfies a large deviation scaling. A notion of subsolution is defined for the related calculus of variations problem, and two main results are proved under mild conditions. The first is that the number of particles generated by the algorithm grows subexponentially if and only if a certain scalar multiple of the importance function is a subsolution. The second is that, under the same condition, the variance of the algorithm is characterized (asymptotically) in terms of the subsolution. The design of asymptotically optimal schemes is discussed, and numerical examples are presented.

Keywords: Rare; event; Monte; Carlo; Branching; process; Large; deviations; Subsolutions; Hamilton-Jacobi-Bellman; equation; Simulation; Variance; reduction (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00059-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:119:y:2009:i:2:p:562-587

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().