Investigation of sample paths properties of sub-Gaussian type random fields, with application to stochasic heat equations

TL;DR

This paper derives bounds for the distribution of maxima of sub-Gaussian random fields with anisotropic metrics and applies these results to stochastic heat equations with fractional noise, providing tail bounds and growth estimates.

Contribution

It introduces new bounds for the suprema of sub-Gaussian fields with anisotropic metrics and applies them to stochastic heat equations with fractional noise.

Findings

Bounds for tail distributions of suprema are established.

Growth rate estimates for stochastic heat fields are provided.

Results enhance understanding of fractional noise effects in heat equations.

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.