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Investigation of sample paths properties of sub-Gaussian type random fields, with application to stochastic heat equations
Olha Hopkalo   Lyudmyla Sakhno  

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https://doi.org/10.15559/25-VMSTA273
Pub. online: 27 February 2025      Type: Research Article      Open accessOpen Access

Received
12 May 2024
Revised
1 December 2024
Accepted
30 January 2025
Published
27 February 2025

Abstract

The paper presents bounds for the distributions of suprema for a particular class of sub-Gaussian type random fields defined over spaces with anisotropic metrics. The results are applied to random fields related to stochastic heat equations with fractional noise: bounds for the tail distributions of suprema and estimates for the rate of growth are provided for such fields.

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Keywords
Sub-Gaussian type random fields distribution of supremum rate of growth stochastic heat equation fractional noise

MSC2010
60G17 60G60 60H15

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