High excursions of Bessel process and other processes of Bessel type

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Abstract

A high excursion probability for the modulus of a Gaussian vector process with independent identically distributed components is evaluated. It is assumed that the components have means zero and variances reaching its absolute maximum at a single point of the considered time interval. An important example of such processes is the Bessel process.

About the authors

V. I. Piterbarg

Lomonosov Moscow State University; Federal State Institution «Scientific Research Institute for System Analysis of the Russian Academy of Sciences»

Author for correspondence.
Email: piter@mech.math.msu.su
Russian Federation, 1, Leninskie gory, Moscow, 119991; 36-1, Nakhimovsky prospect, Moscow, 117218

I. V. Rodionov

Institute of Control Sciences of the Russian Academy of Sciences; Moscow Institute of Physics and Technology

Email: vecsell@gmail.com
Russian Federation, 65, Profsoyuznaya Street, Moscow, 117997; 9, Institutskij, Dolgoprudny, Moscow region, 141701

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