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Modern Stochastics: Theory and Applications


Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes
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Volume 8, Issue 1 (2023), pp. 41–62
Pub. online: 26 January 2021      Type: Research Article      Open accessOpen Access
Received
7 September 2020
Revised
21 December 2020
Accepted
7 January 2021
Published
26 January 2021

Abstract

This paper investigates sample paths properties of φ-sub-Gaussian processes by means of entropy methods. Basing on a particular entropy integral, we treat the questions on continuity and the rate of growth of sample paths. The obtained results are then used to investigate the sample paths properties for a particular class of φ-sub-Gaussian processes related to the random heat equation. We derive the estimates for the distribution of suprema of such processes and evaluate their rate of growth.

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Keywords
φ-sub-Gaussian processes distribution of sumpremum rate of growth entropy methods heat equation random initial conditions

MSC2010
35G10 35R60 60G20 60G60

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