|
|
- 2015
一类倒向随机微分方程解的稳定性定理
|
Abstract:
摘要： 通过建立两个等价概率测度下随机变量条件数学期望之间的一个不等式, 在生成元g关于y单调且关于z一致连续的条件下证明了倒向随机微分方程解的一个稳定性定理, 推广了几个已知的结果。
Abstract: By establishing an inequality between conditional mathematic expectations of random variables under two different but equivalent probability measures, we prove a stability theorem for solutions of backward stochastic differential equations whose generator g is monotonic in y and uniformly continuous in z,which generalizes some known results
| [1] | JIA Guangyan. Backward stochastic differential equations with a uniformly continuous generator and related g-expectation [J]. Stochastic Processes and Their Applications, 2010, 120(11):2241-2257. |
| [2] | PARDOUX E, PENG Shige. Adapted solution of a backward stochastic differential equation [J]. Systems Control Letters, 1990, 14(1):55-61. |
| [3] | PARDOUX E. BSDEs, weak convergence and homogenization of semilinear PDEs [J]. Nonlinear Analysis, Differential Equations and Control, 1999, 528:503-549. |
| [4] | ？KSENDAL B. Stochastic differential equations: an introduction with applications [M]. Berlin Heidelberg: Springer, 2003:154-155. |
| [5] | El KAROUI N, PENG Shige. Backward stochastic differential equations in finance [J]. Mathematical Finance, 1997, 7(1):1-72. |
| [6] | FAN Shengjun, JIANG Long. Uniqueness result for the BSDE whose generator is monotonic in y and uniformly continuous in z[J]. C R Acad Sci Paris: Ser I, 2010, 348(1-2):89-92. |
| [7] | FAN Shengjun, JIANG Long. Existence and uniqueness result for a backward stochastic differential equation whose generator is Lipschitz continuous in y and uniformly continuous in z[J]. Journal of Applied Mathematics and Computing, 2010, 36(1-2):1-10. |
