$G$-Bessel processes and related properties

Abstract

In this paper, we introduce $G$-Bessel processes for a class of $d$-dimensional $G$-Brownian motions. Under the condition of dimensionality $d$, we obtain that the $G$-Bessel process is the solution of the stochastic differential equation. Furthermore, under the stricter condition of dimensionality, we establish the existence and uniqueness of a solution of the stochastic differential equation governing the $G$-Bessel process and prove the nonattainability of the origin for $G$-Brownian motion.