Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation
Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation
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DOI：
10.1016/j.spa.2007.10.015
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发表时间：
2008-12-01
影响因子：
1.4
通讯作者：
Peng, Shige
中科院分区：
文献类型：
--
作者：
Peng, Shige
本文提出了由具有无穷小生成元G的非线性热方程生成的非线性期望-G-期望的概念。我们首先研究多维G-正态分布。有了这个非线性分布，我们可以引入我们的G-期望，在这个期望下，正则过程是一个多维G-布朗运动。然后，我们建立了相关的随机微积分，特别是伊藤型的随机积分关于我们的G-布朗运动，并推导出相关的伊藤公式。我们还得到了随机微分方程在我们的G-期望下解的存在唯一性。(C)2008 Elsevier B. V.保留所有权利。
We develop a notion of nonlinear expectation - G-expectation - generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce Our G-expectation under which the canonical process is a multi-dimensional G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Ito's type with respect to Our G-Brownian motion, and derive the related Ito's formula. We have also obtained the existence and uniqueness of stochastic differential equations under Our G-expectation. (C) 2008 Elsevier B.V. All rights reserved.