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Large Deviations of a Storage Process with Fractional Brownian Motion as Input

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Abstract

We study probabilities of large extremes of the storage process Y(t) = sup σ≥t (X(σ) - X(t) - c(σ - t)), where X(t) is the fractional Brownian motion. We derive asymptotic behavior of the maximum tail distribution for the process on fixed or slowly increased intervals by a reduction the problem to a large extremes problem for a Gaussian field.

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Authors and Affiliations

  1. Moscow Lomonosov State University, Russia

    Vladimir I. Piterbarg

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  1. Vladimir I. Piterbarg
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Piterbarg, V.I. Large Deviations of a Storage Process with Fractional Brownian Motion as Input. Extremes 4, 147–164 (2001). https://doi.org/10.1023/A:1013973109998

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  • DOI: https://doi.org/10.1023/A:1013973109998

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