6 citations · 14 across the 11 of their papers we have counts for
6 papers · 1 filter
Exit times for semimartingales under nonlinear expectation
Guomin Liu
Let be the upper expectation of a weakly compact but non-dominated family of probability measures. Assume that is a -dimensional $\mathcal{P…
Multi-dimensional BSDEs driven by -Brownian motion and related system of fully nonlinear PDEs
Guomin Liu
In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by -Brownian motion (-BSDEs) with diagonal generators, the $…
Girsanov formula for -Brownian motion: the degenerate case
Guomin Liu
In this paper, we prove the Girsanov formula for -Brownian motion without the non-degenerate condition. The proof is based on the perturbation method in the nonlinear setting by…
Local time and Tanaka formula of -martingales
Guomin Liu
The objective of this paper is to study the local time and Tanaka formula of symmetric -martingales. We introduce the local time of -martingales and show that they belong to…
Lévy's martingale characterization and reflection principle of -Brownian motion
Mingshang Hu, Xiaojun Ji, Guomin Liu
In this paper, we obtain Lévy's martingale characterization of -Brownian motion without the nondegenerate condition. Base on this characterization, we prove the reflection princ…
On the exit times of SDEs driven by -Brownian motion
Guomin Liu, Shige Peng, Falei Wang
This paper is devoted to studying the properties of the exit times of stochastic differential equations driven by -Brownian motion (-SDEs). In particular, we prove that the e…