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June 2011 Efficient simulation for the maximum of infinite horizon discrete-time Gaussian processes
Jose Blanchet, Chenxin Li
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J. Appl. Probab. 48(2): 467-489 (June 2011). DOI: 10.1239/jap/1308662639


We consider the problem of estimating the probability that the maximum of a Gaussian process with negative mean and indexed by positive integers reaches a high level, say b. In great generality such a probability converges to 0 exponentially fast in a power of b. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we develop an importance sampling procedure, called the target bridge sampler (TBS), which takes a polynomial (in b) number of function evaluations to achieve a small relative error. The procedure also yields samples of the underlying process conditioned on hitting b in finite time. In addition, we apply our method to the problem of estimating the tail of the maximum of a superposition of a large number, n, of independent Gaussian sources. In this situation TBS achieves a prescribed relative error with a bounded number of function evaluations as n ↗ ∞. A remarkable feature of TBS is that it is not based on exponential changes of measure. Our numerical experiments validate the performance indicated by our theoretical findings.


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Jose Blanchet. Chenxin Li. "Efficient simulation for the maximum of infinite horizon discrete-time Gaussian processes." J. Appl. Probab. 48 (2) 467 - 489, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1219.65012
MathSciNet: MR2840311
Digital Object Identifier: 10.1239/jap/1308662639

Primary: 65C05
Secondary: 60F10 , 60G15

Keywords: fractional Brownian noise , Gaussian process , importance sampling , large deviations , rare-event simulation

Rights: Copyright © 2011 Applied Probability Trust


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Vol.48 • No. 2 • June 2011
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