A study on the fractional Gruschin type process

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.