Rare event simulation. (English) Zbl 1101.65005
The paper is focused on the simulation approach based on the Monte Carlo method. It is used to estimate the probabilities of rare events. Fast simulation based on a splitting method is applied to minimize the variance of the estimator. With this technique (called REpetitive Simulation Trails After Reaching Thresholds – RESTART), the space state is partitioned into a series of nested subsets, and the rare events are considered in this context as a nested sequence of events. When a given subset is entered by a sample trajectory, random retrials are generated from the initial state corresponding to the state of the system at the entry point. Thus, the system trajectory is split into a number of new subtrajectories.
A simple model of splitting is build to introduce a new estimator and to analyze the behavior of the rare event probability. An optimization of the proposed algorithm is accomplished, and a precise confidence interval of the estimator is obtained, using a branching process. Finally, a discussion of the merits of the proposed approach and further research direction are discussed and overall conclusions are presented.
A simple model of splitting is build to introduce a new estimator and to analyze the behavior of the rare event probability. An optimization of the proposed algorithm is accomplished, and a precise confidence interval of the estimator is obtained, using a branching process. Finally, a discussion of the merits of the proposed approach and further research direction are discussed and overall conclusions are presented.
Reviewer: Tzvetan Semerdjiev (Sofia)
MSC:
65C20 | Probabilistic models, generic numerical methods in probability and statistics |
65C05 | Monte Carlo methods |
62F25 | Parametric tolerance and confidence regions |
65C60 | Computational problems in statistics (MSC2010) |
Keywords:
Monte Carlo method; repetitive simulation trails after reaching thresholds; RESTART; rare event probability; algorithm; confidence intervalReferences:
[1] | Cosnard, Annales des sciences mathématiques du Québec 8 pp 5– (1984) |
[2] | DOI: 10.1214/aoap/1034968137 · Zbl 0855.60031 · doi:10.1214/aoap/1034968137 |
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