Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation
Abstract
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 Itô's type with respect to our G-Brownian motion, and derive the related Itô's formula. We have also obtained the existence and uniqueness of stochastic differential equations under our G-expectation.Download Info
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Bibliographic Info
Article provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 118 (2008)
Issue (Month): 12 (December)
Pages: 2223-2253
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Related research
Keywords: g-expectation G-expectation G-normal distribution BSDE SDE Nonlinear probability theory Nonlinear expectation Brownian motion Ito's stochastic calculus Ito's integral Ito's formula Gaussian process Quadratic variation process Jensen's inequality G-convexity;References
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Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Moreau, Ludovic, 2012. "A contribution in stochastic control applied to finance and insurance," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/10711, Université Paris-Dauphine.
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