$ G $-Bessel processes and related properties

Mingshang Hu, Renxing Li

Published 2024-04-19Version 1

In this paper, for a class of $ d $-dimensional $ G $-Brownian motions, we introduce $ G $-Bessel processes. Under the condition of dimensionality $ d $, we obtain that the $ G $-Bessel process is the solution of a stochastic differential equation. Moreover, under the more strict condition of dimensionality $ d $, we get the uniqueness of the solution of stochastic differential equations governing $ G $-Bessel processes and the nonattainability of the origin of $ G $-Brownian motion.