Quasi-continuous random variables and processes under the G-expectation framework

Abstract

In this paper, we first use PDE techniques and probabilistic methods to identify a kind of quasi-continuous random variables. Then we give a characterization of the $G$-integrable processes and get a kind of quasi-continuous processes by Krylov's estimates. This result is useful for the development of $G$-stochastic analysis theory. Moreover, it also provides a tool for the study of the non-Markovian Itô processes.

22 pages

Cited by in corpus (2)

• Lévy's martingale characterization and reflection principle of $G$-Brownian motion
• Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation