Invariant and ergodic nonlinear expectations for $G$-diffusion processes
Invariant and ergodic nonlinear expectations for $G$-diffusion processes
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DOI：
10.1214/ecp.v20-3886
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发表时间：
2015-03
影响因子：
0.5
通讯作者：
Mingshang Hu;Hanwu Li;Falei Wang;Guoqiang Zheng
中科院分区：
文献类型：
--
作者：
Mingshang Hu;Hanwu Li;Falei Wang;Guoqiang Zheng
本文在G-期望框架下研究了不变期望和遍历期望问题。特别地，由G-布朗运动驱动的随机微分方程（G-SDEs）具有唯一的不变期望和遍历期望。此外，不变和遍历期望的G-SDES也是次线性期望。然而，不变期望与遍历期望不一定一致，这与经典情形不同。
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 (G-SDEs) 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.