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

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  • Gao, Fuqing

Abstract

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 Itô's formula for the G-stochastic integrals. Some moment estimates and Hölder 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.

Suggested Citation

  • Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3356-3382
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    References listed on IDEAS

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    1. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    2. Xu, Jing & Zhang, Bo, 2009. "Martingale characterization of G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 232-248, January.
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