数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 872-882.doi: 10.1016/S0252-9602(13)60047-8

• 论文 • 上一篇    

REGULARITY PROPERTY OF SOLUTION TO TWO-PARAMETER STOCHASTIC VOLTERRA EQUATION WITH NON-LIPSCHITZ COEFFICIENTS

姜国|王湘君*   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
    School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China; School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:2012-09-06 出版日期:2013-05-20 发布日期:2013-05-20
  • 通讯作者: 王湘君,x.j.wang@163.com E-mail:jg1996@126.com;x.j.wang@163.com
  • 基金资助:

    This work is supported by NSF (10971076 and 11061032) of China and Science and Technology Research Projects of Hubei Provincial Department of Education (Q20132505).

REGULARITY PROPERTY OF SOLUTION TO TWO-PARAMETER STOCHASTIC VOLTERRA EQUATION WITH NON-LIPSCHITZ COEFFICIENTS

 JIANG Guo, WANG Xiang-Jun*   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
    School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China; School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2012-09-06 Online:2013-05-20 Published:2013-05-20
  • Contact: WANG Xiang-Jun,x.j.wang@163.com E-mail:jg1996@126.com;x.j.wang@163.com
  • Supported by:

    This work is supported by NSF (10971076 and 11061032) of China and Science and Technology Research Projects of Hubei Provincial Department of Education (Q20132505).

摘要:

This article proves the existence and uniqueness of solution to two-parameter stochastic Volterra equation with non-Lipschitz coefficients and driven by Brownian sheet, where the main tool is Bihari´s inequality in the plane. Moreover, we also discuss the time regularity property of the solution by Kolmogorov´s continuity criterion.

关键词: Stochastic Volterra equation, Brownian sheet, Bihari´s inequality, non-Lipschitz, Picard´s approximation

Abstract:

This article proves the existence and uniqueness of solution to two-parameter stochastic Volterra equation with non-Lipschitz coefficients and driven by Brownian sheet, where the main tool is Bihari’s inequality in the plane. Moreover, we also discuss the time regularity property of the solution by Kolmogorov´s continuity criterion.

Key words: Stochastic Volterra equation, Brownian sheet, Bihari´s inequality, non-Lipschitz, Picard´s approximation

中图分类号: 

  • 60H20