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High excursions of Bessel and related random processes

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  • Piterbarg, Vladimir I.
  • Rodionov, Igor V.

Abstract

Asymptotic behavior of large excursions probabilities is evaluated for Euclidean norm of a wide class of Gaussian non-stationary vector processes with independent identically distributed components. It is assumed that the components have means zero and variances reaching its absolute maximum at only one point of the considered time interval. The Bessel process is an important example of such processes.

Suggested Citation

  • Piterbarg, Vladimir I. & Rodionov, Igor V., 2020. "High excursions of Bessel and related random processes," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4859-4872.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:8:p:4859-4872
    DOI: 10.1016/j.spa.2020.02.002
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    References listed on IDEAS

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    1. Estrella, Arturo, 2003. "Critical Values And P Values Of Bessel Process Distributions: Computation And Application To Structural Break Tests," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1128-1143, December.
    2. Liu, Peng & Ji, Lanpeng, 2017. "Extremes of locally stationary chi-square processes with trend," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 497-525.
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