Investigation Of Sample Paths Properties For Some Classes Of Phi-Sub-Gaussian Stochastic Processes

This paper investigates sample paths properties of phi-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 phi-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.