A study on the fractional Gruschin type process

TL;DR

This paper develops derivative formulas and gradient estimates for fractional Gruschin type processes, extending previous Markovian results to a non-Markovian setting using fractional calculus techniques.

Contribution

It introduces new derivative formulas and gradient estimates for fractional Gruschin processes in a non-Markovian context, generalizing earlier Markovian results.

Findings

Derived derivative formulas for fractional Gruschin processes

Established gradient estimates using fractional calculus

Extended classical results to non-Markovian processes

Abstract

In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical difficulties appear in the study. Then, using the fractional calculus technique, we also derive the gradient estimate.