Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (3): 872-882.doi: 10.1016/S0252-9602(13)60047-8

• Articles • Previous Articles    

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).

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

CLC Number: 

  • 60H20
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