Moments approach to the concentration properties of truncated variation

TL;DR

This paper introduces a moments-based method to analyze the concentration properties of truncated variation in stochastic processes, especially useful for processes with heavy-tailed distributions.

Contribution

It presents an alternative approach to concentration analysis, extending results to heavy-tailed stochastic processes using moments control.

Findings

Effective moments control technique for concentration analysis

Generalization to heavy-tailed processes demonstrated

Potential for broader applications in stochastic process analysis

Abstract

In this paper we show an alternative approach to the concentration of truncated variation for stochastic processes on a real line. Our method is based on the moments control and can be used to generalize the results to the case of processes with heavy tails.