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Functional solution about stochastic differential equation driven by $G$-Brownian motion
1. | Department of Mathematics, Honghe University, Mengzi, 661199, China, China |
References:
[1] |
W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd edition, Academic Press, Orlando, 1986. |
[2] |
L. Denis, M. Hu and S. Peng, Function spaces and capacity related to a sublinear expectation: Application to $G$-Brownian motion paths, Potential Anal., 34 (2010), 139-161.
doi: 10.1007/s11118-010-9185-x. |
[3] |
H. Doss, Liens entre équations différentielles stochastiques et ordinaires, (French) C. R. Acad. Sci. Paris Sér. A-B, 283 (1976), A939-A942. |
[4] |
F. Gao, Pathwise properties and homeomorphic flows for stochastic differential equations driven by $G$-Brownian motion, Stoch. Proc. Appl., 119 (2009), 3356-3382.
doi: 10.1016/j.spa.2009.05.010. |
[5] |
M. Hu, S. Ji, S. Peng and Y. Song, Backward stochastic differential equations driven by $G$-Brownian motion, Stochastic Process. Appl., 124 (2014), 759-784.
doi: 10.1016/j.spa.2013.09.010. |
[6] |
K. Itô, On stochastic differential equations, Mem. Amer. Math. Soc., 1951 (1951), 51 pp. |
[7] |
X. Li and S. Peng, Stopping times and related Itô's calculus with $G$-Brownian motion, Stoch. Proc. Appl., 121 (2011), 1492-1508.
doi: 10.1016/j.spa.2011.03.009. |
[8] |
B. Øksendal, Stochastic Differential Equations. An Introduction with Applications, Sixth edition, Springer-Verlag, Berlin, 2003.
doi: 10.1007/978-3-642-14394-6. |
[9] |
S. Peng, $G$-expectation, $G$-Brownian motion and related stochastic calculus of Itô's type, in Stochastic Analysis and Applications (eds. Benth, et al.), Springer-Verlag, 2007, 541-567.
doi: 10.1007/978-3-540-70847-6_25. |
[10] |
S. Peng, Nonlinear expectations and stochastic calculus under uncertainty-with robust central limit theorem and $G$-Brownian motion, preprint, arXiv:1002.4546v1. |
[11] |
H. M. Soner, N. Touzi and J. Zhang, Martingale representation theorem for the $G$-expectation, Stoch. Proc. Appl., 121 (2011), 265-287.
doi: 10.1016/j.spa.2010.10.006. |
[12] |
J. Xu and B. Zhang, Martingale characterization of $G$-Brownian motion, Stoch. Proc. Appl., 119 (2009), 232-248.
doi: 10.1016/j.spa.2008.02.001. |
show all references
References:
[1] |
W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd edition, Academic Press, Orlando, 1986. |
[2] |
L. Denis, M. Hu and S. Peng, Function spaces and capacity related to a sublinear expectation: Application to $G$-Brownian motion paths, Potential Anal., 34 (2010), 139-161.
doi: 10.1007/s11118-010-9185-x. |
[3] |
H. Doss, Liens entre équations différentielles stochastiques et ordinaires, (French) C. R. Acad. Sci. Paris Sér. A-B, 283 (1976), A939-A942. |
[4] |
F. Gao, Pathwise properties and homeomorphic flows for stochastic differential equations driven by $G$-Brownian motion, Stoch. Proc. Appl., 119 (2009), 3356-3382.
doi: 10.1016/j.spa.2009.05.010. |
[5] |
M. Hu, S. Ji, S. Peng and Y. Song, Backward stochastic differential equations driven by $G$-Brownian motion, Stochastic Process. Appl., 124 (2014), 759-784.
doi: 10.1016/j.spa.2013.09.010. |
[6] |
K. Itô, On stochastic differential equations, Mem. Amer. Math. Soc., 1951 (1951), 51 pp. |
[7] |
X. Li and S. Peng, Stopping times and related Itô's calculus with $G$-Brownian motion, Stoch. Proc. Appl., 121 (2011), 1492-1508.
doi: 10.1016/j.spa.2011.03.009. |
[8] |
B. Øksendal, Stochastic Differential Equations. An Introduction with Applications, Sixth edition, Springer-Verlag, Berlin, 2003.
doi: 10.1007/978-3-642-14394-6. |
[9] |
S. Peng, $G$-expectation, $G$-Brownian motion and related stochastic calculus of Itô's type, in Stochastic Analysis and Applications (eds. Benth, et al.), Springer-Verlag, 2007, 541-567.
doi: 10.1007/978-3-540-70847-6_25. |
[10] |
S. Peng, Nonlinear expectations and stochastic calculus under uncertainty-with robust central limit theorem and $G$-Brownian motion, preprint, arXiv:1002.4546v1. |
[11] |
H. M. Soner, N. Touzi and J. Zhang, Martingale representation theorem for the $G$-expectation, Stoch. Proc. Appl., 121 (2011), 265-287.
doi: 10.1016/j.spa.2010.10.006. |
[12] |
J. Xu and B. Zhang, Martingale characterization of $G$-Brownian motion, Stoch. Proc. Appl., 119 (2009), 232-248.
doi: 10.1016/j.spa.2008.02.001. |
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