$ G $-Bessel processes and related properties

TL;DR

This paper introduces G-Bessel processes linked to d-dimensional G-Brownian motions, establishing their solutions to stochastic differential equations and proving properties like nonattainability of the origin.

Contribution

It defines G-Bessel processes within the G-Brownian motion framework and proves existence, uniqueness, and nonattainability results for these processes.

Findings

G-Bessel processes are solutions to specific stochastic differential equations.

Existence and uniqueness of solutions are established under certain conditions.

The origin is proven to be nonattainable for G-Brownian motion.

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.