Tail estimates for Markovian rough paths

TL;DR

This paper establishes improved tail estimates for the accumulated local p-variation of Markovian rough paths, which has implications for understanding the behavior of stochastic processes related to subelliptic Dirichlet forms.

Contribution

It provides a better-than-exponential tail estimate for the accumulated local p-variation in the context of Markovian rough paths, advancing the theoretical understanding of these stochastic processes.

Findings

Proved better-than-exponential tail bounds for local p-variation

Connected tail estimates to problems in rough path theory and stochastic analysis

Commented on implications for recent research by Chevyrev and Lyons

Abstract

We work in the context of Markovian rough paths associated to a class of uniformly subelliptic Dirichlet forms [25] and prove a better-than-exponential tail estimate for the accummulated local p-variation functional, which has been introduced and studied in [17]. We comment on the significance of these estimates to a range of currently-studied problems, including the recent results of Chevyrev and Lyons in [18].