Harnack Inequality and Applications for SDEs Driven by $G$-Brownian motion

Abstract

We establish Harnack inequality and shift Harnack inequality for stochastic differential equation driven by $G$-Brownian motion. As applications, the uniqueness of invariant linear expectations and estimates on the $\sup$-kernel are investigated, where the $\sup$-kernel is introduced in this paper for the first time.

References in corpus (1)

• Girsanov's formula for G-Brownian motion

Cited by in corpus (2)

• Harnack Inequality and Gradient Estimate for $G$-SDEs with Degenerate Noise
• Harnack and log Harnack Inequalities for $G$-SDEs with Multiplicative Noise