Chaining Techniques and their Application to Stochastic Flows

TL;DR

This paper reviews various chaining methods for estimating properties of stochastic processes and demonstrates their application in bounding the growth of sets under stochastic flows.

Contribution

It introduces a comprehensive review of chaining techniques and applies them to analyze the behavior of stochastic flows.

Findings

Chaining methods effectively estimate supremum and modulus of continuity.

Application of chaining techniques yields bounds on set growth in stochastic flows.

The paper compares different chaining approaches for stochastic process analysis.

Abstract

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can be applied to obtain upper bounds for the growth of bounded sets under the action of a stochastic flow.