Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion

By Fuqing Gao. 2009

244 citations recorded by the source corpus.

We study pathwise properties and homeomorphic property with respect to the initial values for stochastic differential equations driven by G-Brownian motion. We first present a Burkholder-Davis-Gundy inequality and an extension of Ito's formula for the G-stochastic integrals. Some moment estimates and Holder continuity of the G-stochastic integrals and the solutions of stochastic differential equations with Lipschitzian coefficients driven by G-Brownian motion are obtained. Homeomorphic property with respect to the initial values is also established.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ba81bbe91fa0eb1f63e3d23a0c9b138d77d9142e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

1. Yiqing Lin
2. Xinpeng Li
3. Xiangyun Lin
4. Xue-peng Bai
5. Yong Ren
6. Rathinasamy Sakthivel
7. Shige Peng
8. X. Jia

In Finance

1. Yiqing Lin
2. Rathinasamy Sakthivel
3. Yong Ren
4. Xue-peng Bai
5. Xinpeng Li
6. X. Jia
7. Xinpeng Li
8. Xiangyun Lin

In Management Science and Operations Research

1. Yiqing Lin
2. Xinpeng Li
3. Xiangyun Lin
4. Shige Peng
5. Xinpeng Li
6. Yong Ren
7. Rathinasamy Sakthivel
8. X. Jia

Citations in the corpus

• Lyapunov-type conditions and stochastic differential equations driven by $G$-Brownian motion (2014, methodology): “The reader interested in more detailed description of these notions and results is referred to Denis-Hu-Peng [4], Gao [5], Li-Peng [8] and Peng [12].”
• Stopping times and related Itô's calculus with G-Brownian motion (2009, methodology): “Recently Gao [7] has improved the Itô’s formula of Peng.”
• On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients (2010, background): “As a counterpart in the classical framework, stochastic differential equations driven by G-Brownian motion (GSDEs) have been studied by Gao[4] and Peng[10].”
• Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010, background): “Gao (2009)[54] proved a more general Itô’s formula for G-Brownian motion.”
• The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion (2017, methodology): “We refer the readers to Gao [7], Lin [8], Ren et al. [9], Ren and Hu [10] and the references therein.”
• Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, methodology): “The following form of Itô’s formula was obtained by Peng (2006a) and improved by Gao (2009).”