Squared Bessel processes under nonlinear expectation
Probability
2026-01-21 v2
Abstract
In this paper, we define the squared G-Bessel process as the square of the modulus of a class of G-Brownian motions and establish that it is the unique solution to a stochastic differential equation. We then derive several path properties of the squared G-Bessel process, which are more profound in the capacity sense. Furthermore, we provide upper and lower bounds for the Laplace transform of the squared G-Bessel process. Finally, we prove that the time-space transformed squared G-Bessel process is a G'-CIR process.
Cite
@article{arxiv.2509.24481,
title = {Squared Bessel processes under nonlinear expectation},
author = {Mingshang Hu and Renxing Li and Xue Zhang},
journal= {arXiv preprint arXiv:2509.24481},
year = {2026}
}