H{\"o}lder continuity of random processes

TL;DR

This paper establishes Hölder continuity for specific classes of stochastic processes with bounded increments, extending previous results by Kwapien and Rosinski through advanced probabilistic methods.

Contribution

It generalizes existing theorems on sample Hölder continuity and majorizing measures for stochastic processes with bounded increments.

Findings

Proves Hölder continuity for certain classes of processes.

Extends results of Kwapien and Rosinski.

Provides a broader framework for stochastic process regularity.

Abstract

The paper will be published in JOTP. In the paper we prove Holder Continuity for ceratian classes of processes with bounded increments. The paper generalizes results obtained by Kwapien and Rosinski in Sample H{\"o}lder continuity of stochastic processes and majorizing measures. \textit{Seminar on Stochastic Analysis, Random Fields and Applications IV, Progr. in Probab.} {\bf 58}, 155--163. Birkh{\"a}user, Basel.