Blanchet J, Li C. Efficient Simulation for the Maximum of Infinite Horizon Discrete-Time Gaussian Processes. Journal of Applied Probability. 2011;48(2):467-489. doi:10.1239/jap/1308662639

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Abstract

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 …
Authors
Jose Blanchet, Chenxin Li
Publication date
2011/6
Journal
Journal of Applied Probability
Volume
48
Issue
2
Pages
467-489
Publisher
Cambridge University Press