Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 520-556.
Previous Articles Next Articles
Wong-Zakai Approximations of Anticipated Backward Doubly Stochastic Differential Equations with Jumps in Non-Lipschitz Conditions
Jie Xu1,*(
),Yanhua Sun2
- 1 College of Mathematics and Information Science, Henan Normal University, Henan Xinxiang 453002
2 School of Mathematical Sciences, Henan Institute of Science and Technology, Henan Xinxiang 453001
-
Received:2020-08-20Online:2022-04-26Published:2022-04-18 -
Contact:Jie Xu E-mail:xujiescu@163.com -
Supported by:the Key Scientific Research Project Plans of Henan Province(21A110011)
CLC Number:
- O221
Cite this article
Jie Xu,Yanhua Sun. Wong-Zakai Approximations of Anticipated Backward Doubly Stochastic Differential Equations with Jumps in Non-Lipschitz Conditions[J].Acta mathematica scientia,Series A, 2022, 42(2): 520-556.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| 1 | Hao T, Li J. Mean-field SDEs with jumps and nonlocal integral-PDEs. Nonlinear Differ Equ Appl, 2016, 23, Article number: 17 |
| 2 |
Hu F , Chen Z . $L^p$ solutions of anticipated backward stochastic differential equations under monotonicity and general increasing conditions. Stochastics : An International Journal of Probability and Stochastic Processes, 2016, 88 (2): 267- 284
doi: 10.1080/17442508.2015.1052810 |
| 3 |
Hu Y , Matoussi A , Zhang T . Wong-Zakai approximations of backward doubly stochastic differential equations. Stochastic Process Appl, 2015, 125: 4375- 4404
doi: 10.1016/j.spa.2015.07.003 |
| 4 | Li S, Xu X. Anticipated backward stochastic differential equations and their applications to zero-sum stochastic differential games. Communications in Statistics-Simulation and Computation, 2019. DOI:10.1080/03610918.2019.1694950 |
| 5 | Ma J , Zhang J . Representation theorems for backward stochastic differential equations. Ann Probab, 2002, 12 (4): 1390- 1418 |
| 6 |
Pardoux E , Peng S . Adapted solution of a backward stochastic differential equation. Systems Control Lett, 1990, 14: 55- 61
doi: 10.1016/0167-6911(90)90082-6 |
| 7 |
Pardoux E , Peng S . Backward doubly SDEs and systems of quasilinear SPDEs. Probab Theory Related Fields, 1994, 98: 209- 227
doi: 10.1007/BF01192514 |
| 8 | Peng S , Yang Z . Anticipated backward stochastic differential equations. Ann Probab, 2009, 37 (3): 877- 902 |
| 9 |
Shen X , Jiang L , Tian D . $L^p$ solutions of anticipated BSDEs with weak monotonicity and general growth generators. Communications in Statistics-Simulation and Computation, 2019, 48 (1): 73- 90
doi: 10.1080/03610918.2017.1373812 |
| 10 | Wen J , Shi Y . Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem. Applied Mathematics and Computation, 2019, 35: 282- 298 |
| 11 |
Wen J , Shi Y . Solvability of anticipated backward stochastic Volterra integral equations. Stat Probabil Lett, 2020, 156: 108599
doi: 10.1016/j.spl.2019.108599 |
| 12 |
Wong E , Zakai M . On the relation between ordinary and stochastic differential equations. Internat J Engrg Sci, 1965, 3: 213- 229
doi: 10.1016/0020-7225(65)90045-5 |
| 13 |
Wu H , Wang W , Ren J . Anticipated backward stochastic equations with non-Lipschitz coefficients. Stat Probabil Lett, 2012, 82: 672- 682
doi: 10.1016/j.spl.2011.12.008 |
| 14 |
Xu W . Backward doubly stochastic equations with jumps and comparision theorems. J Math Anal Appl, 2016, 443 (1): 596- 624
doi: 10.1016/j.jmaa.2016.05.050 |
| 15 | Xu X . Anticipated backward doubly stochastic differential equations. Appl Math Comput, 2013, 220: 53- 62 |
| 16 | Yang Z , Elliott R . Some properties of generalized anticipated backward stochastic differential equations. Electron Commun Probab, 2013, 18 (63): 1- 10 |
| 17 |
Zhang T . Wong-Zakai approximations to SDEs with reflection. Potential Anal, 2014, 41 (3): 783- 815
doi: 10.1007/s11118-014-9394-9 |
| 18 |
Zhu Q , Shi Y . Backward doubly stochastic differential equations with jumps and stochastic partial differential-integral equations. Chin Ann Math Ser B, 2012, 33: 127- 142
doi: 10.1007/s11401-011-0686-8 |
| [1] | Chen Hongye, Fang Donghui, Wu Kexing. Optimality Conditions and Total Lagrange Dualities for Evenly Convex Optimization Problems [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1255-1267. |
| [2] | Ran Bo,Sun Xiangkai,Guo Xiaole. On Robust Optimal Solutions for a Class of Uncertain Fractional Polynomial Optimization Problems [J]. Acta mathematica scientia,Series A, 2025, 45(2): 630-639. |
| [3] | Shen Zongshan. Stability of Error Bounds for Multifunctions [J]. Acta mathematica scientia,Series A, 2025, 45(1): 214-235. |
| [4] | Fan Tiantian, Tang Jingyong, Zhou Jinchuan. Nonmonotone Smoothing Inexact Newton Algorithm for Solving Weighted Horizontal Linear Complementarity Problems [J]. Acta mathematica scientia,Series A, 2025, 45(1): 165-179. |
| [5] | Jian Jinbao, Dai Yu, Yin Jianghua. An Inertial Conjugate Gradient Projection Method for the Split Feasibility Problem [J]. Acta mathematica scientia,Series A, 2024, 44(4): 1066-1079. |
| [6] | Cai Yu, Zhou Guanghui. Global Convergence of a WYL Type Spectral Conjugate Gradient Method [J]. Acta mathematica scientia,Series A, 2024, 44(1): 173-184. |
| [7] | Huang Jiayi, Sun Xiangkai. Duality Characterizations for a Class of Two-Stage Adjustable Robust Multiobjective Programming [J]. Acta mathematica scientia,Series A, 2024, 44(1): 185-194. |
| [8] | Chen Jianhua, Peng Jianwen. Research on the Convergence Rate of Bregman ADMM for Nonconvex Multiblock Optimization [J]. Acta mathematica scientia,Series A, 2024, 44(1): 195-208. |
| [9] | Huang Xiaomei, Tang Guoji. KKT and Weakly Complementary Approximate KKT Conditions for Interval-Valued Optimization Problems [J]. Acta mathematica scientia,Series A, 2023, 43(6): 1897-1913. |
| [10] | Jian Jinbao,Lin Hui,Ma Guodong. A Splitting Sequence Quadratic Programming Algorithm for the Large-Scale Nonconvex Nonseparable Optimization Problems [J]. Acta mathematica scientia,Series A, 2023, 43(4): 1284-1296. |
| [11] | Yang Lanxiang, Chen Yi, Ye Minglu. Inertial Projection Algorithms for Quasimonotone Variational Inequalities [J]. Acta mathematica scientia,Series A, 2023, 43(2): 593-603. |
| [12] | Liu Pengjie, Wu Yanqiang, Shao Feng, Zhang Yan, Shao Hu. Two Extended HS-type Conjugate Gradient Methods with Restart Directions [J]. Acta mathematica scientia,Series A, 2023, 43(2): 570-580. |
| [13] | Liu Fuqin, Peng Jianwen, Luo Honglin. Convergence Analysis of Bregman ADMM for Three-Block Nonconvex Indivisible Optimization Problems with Linearization Technique [J]. Acta mathematica scientia,Series A, 2023, 43(1): 291-304. |
| [14] | Xie Feifei, Fang Donghui. Approximate Farkas Lemma and Approximate Duality for Fractional Optimization Problems [J]. Acta mathematica scientia,Series A, 2023, 43(1): 305-320. |
| [15] | Caiyun Xiao,Xiangkai Sun. Characterization of the Radius of the Robust Feasibility for a Class of Uncertain Convex Optimization Problems with Polynomial Constraints [J]. Acta mathematica scientia,Series A, 2022, 42(5): 1551-1559. |
|