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On the Maximum of a Gaussian Process with Unique Maximum Point of its Variance

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Abstract

Gaussian random processes whose variances reach their maximum values at unique points are considered. Exact asymptotic behavior of probabilities of large absolute maximums of their trajectories have been evaluated using the double sum method under the widest possible conditions.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    S. G. Kobelkov & V. I. Piterbarg

  2. National Research University Higher School of Economics, Moscow, Russia

    V. I. Piterbarg

  3. Scientific Research Institute of System Development “NIISI RAS”, Moscow, Russia

    V. I. Piterbarg

  4. Trapeznikov Institute of Control Sciences of RAS, Moscow, Russia

    I. V. Rodionov

  5. University of Lausanne, 1015, Lausanne, Suisse

    E. Hashorva

Authors
  1. S. G. Kobelkov
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  2. V. I. Piterbarg
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  3. I. V. Rodionov
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  4. E. Hashorva
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Corresponding author

Correspondence to S. G. Kobelkov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 1, pp. 161–174, 2020.

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Kobelkov, S.G., Piterbarg, V.I., Rodionov, I.V. et al. On the Maximum of a Gaussian Process with Unique Maximum Point of its Variance. J Math Sci 262, 504–513 (2022). https://doi.org/10.1007/s10958-022-05831-x

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  • DOI: https://doi.org/10.1007/s10958-022-05831-x

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