Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes

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.

Keywords

• <italic>φ</italic>-sub-Gaussian processes
• distribution of sumpremum
• rate of growth
• entropy methods
• Heat equation
• random initial conditions