[1]袁明霞,王丙均,肖庆坤.由G-布朗运动驱动的具有一致连续性生成元的BSDE的解的极限定理[J].南京师大学报(自然科学版),2023,46(01):11-17.[doi:10.3969/j.issn.1001-4616.2023.01.003]
　Yuan Mingxia,Wang Bingjun,Xiao Qingkun.A Limit Theorem for Solutions of BSDEs Driven by G-Brownian Motion with Uniformly Continuous Generators[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(01):11-17.[doi:10.3969/j.issn.1001-4616.2023.01.003]
点击复制

由G-布朗运动驱动的具有一致连续性生成元的BSDE的解的极限定理()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年01期
页码:
11-17
栏目:
数学
出版日期:
2023-03-15

文章信息/Info

Title:
A Limit Theorem for Solutions of BSDEs Driven by G-Brownian Motion with Uniformly Continuous Generators
文章编号:
1001-4616(2023)01-0011-07
作者:
袁明霞1; 王丙均2; 肖庆坤3
(1.南京交通职业技术学院基础部，江苏 南京 211188)
(2.金陵科技学院理学院，江苏 南京 211169)
(3.南京农业大学理学院，江苏 南京 210095)
Author(s):
Yuan Mingxia1; Wang Bingjun2; Xiao Qingkun3
(1.Basic Department, Nanjing Vocational Institute of Transport Technology, Nanjing 211188, China)
(2.College of Science, Jinling Institute of Technology, Nanjing 211169, China)
(3.College of Science, Nanjing Agricultural University, Nanjing 210095, China)
关键词:
极限定理; G-布朗运动; 一致连续生成元
Keywords:
limit theorem;  G-Brownian motion;  uniformly continuous generators
分类号:
O175.29; O211.6
DOI:
10.3969/j.issn.1001-4616.2023.01.003
文献标志码:
A
摘要:
研究了由G-布朗运动驱动的具有一致连续性生成元的倒向随机微分方程的解的极限定理,并由此得到了该方程的逆比较定理.
Abstract:
In this paper,we study the limit theorem for solutions of BSDEs driven by G-Brownian motion with uniformly continuous generators and then we use the representation theorem to get a converse comparison theorem for GBSDEs with uniformly continuous generators.

参考文献/References:

[1]PENG S. Nonlinear expectations and stochastic calculus under uncertainly. With robust CLT and G-Brownian motion[EB/OL]. Probability Theory and Stochastic Modelling,95. Springer,Berlin(2019). Xiii+212 pp. ISBN:978-3-662-59902-0; 978-3-662-59903-7 60-02(39A50 60-01 60Fxx 60Hxx).
[2]PENG S. G-expectation,G-Brownian motion and realted stochastic calculus of Itô type[C]//Stochastic Analysis and Applications. Abel Symposium,Springer,Berlin,2007,2:541-567.
[3]DENIS L,HU M,PENG S. Function spaces and capacity related to a sublinear expectation:application to G-Brownain motion paths[J]. Potential Anal.,2011,34:139-161.
[4]GAO F Q. Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion[J]. Stochastic Process. Appl.,2009,119:3356-3382.
[5]HU M,WANG F,ZHENG G. Quasi-continuous random variables and processes under the G-expectation framework[J]. Stochastic Process. Appl.,2016,126:2367-2387.
[6]HU M,JI S,PENG S,SONG Y. Backward stochastic differential equation driven by G-Brownian motion[J]. Stochastic Process. Appl.,2014,124:759-784.
[7]HEAND K,HU M. Represnetation theorem for generators of BSDEs driven by G-Brownian motion and its applications[J]. Abstr. Appl. Anal.,2013,1:1-10.
[8]WANG F,ZHENG G. Backward stochastic differential equations driven by G-Brownian motion with uniformly continuous generators[J],J. Theoret. Probab.,2020,Doi:10.1007/s10959-020-00998-y.
[9]LI X,PENG S. Stopping times and related Ito'scalculus with G-Brownian motion[J]. Stochastic Process. Appl.,2011,121:1492-1508.
[10]LEPELTIER J,SAN MARTIN J. Backward stochastic differential equations with continuous coefficients[J]. Statist. Probab. Lett.,1997,34:425-430.
[11]GENG X,QIAN Z,YANG D. G-Brownian motion as rough paths and differential equations driven by G-Brownian motion as rough paths and differential equations driven by ownian motion[M]. Sminaire de Probabilits XLVI. Cham,Heidelberg,New York,Dordrecht London:Springer,2014:125-193.(eBook)

备注/Memo

备注/Memo:
收稿日期:2021-02-21.
基金项目:国家自然科学基金项目(11601203、12171084、11801270)、江苏省“大规模复杂系统数值模拟”重点实验室项目(202003)、中央高校基本科研专项资金项目(Kyz201748、Y0201801249)、金陵科技学院校级孵化项目(Jit-fhxm-2021)、金陵科技学院博士启动基金项目(Jit-b-201836).
通讯作者:王丙均,博士,副教授,研究方向:随机微分方程. E-mail:wbj586@126.com
更新日期/Last Update: 2023-03-15