Open Access
2015 Invariant and ergodic nonlinear expectations for $G$-diffusion processes
Mingshang Hu, Hanwu Li, Falei Wang, Guoqiang Zheng
Author Affiliations +
Electron. Commun. Probab. 20: 1-15 (2015). DOI: 10.1214/ECP.v20-3886


In this paper we study the problems of invariant and ergodic expectations under $G$-expectation framework. In particular, the stochastic differential equations driven by $G$-Brownian motion have the unique invariant and ergodic expectations. Moreover, the invariant and ergodic expectations of $G$-SDEs are also sublinear expectations. However, the invariant expectations may not coincide with the ergodic expectations, which is different from the classical case.


Download Citation

Mingshang Hu. Hanwu Li. Falei Wang. Guoqiang Zheng. "Invariant and ergodic nonlinear expectations for $G$-diffusion processes." Electron. Commun. Probab. 20 1 - 15, 2015.


Accepted: 29 March 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1321.60153
MathSciNet: MR3327869
Digital Object Identifier: 10.1214/ECP.v20-3886

Primary: 60H10
Secondary: 60H30

Keywords: $G$-diffusion process , ergodic expectation , invariant expectation

Back to Top