Articles

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

  • JIANG Guo ,
  • WANG Xiang-Jun
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  • 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 date: 2012-09-06

  Online published: 2013-05-20

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.

Cite this article

JIANG Guo , WANG Xiang-Jun . REGULARITY PROPERTY OF SOLUTION TO TWO-PARAMETER STOCHASTIC VOLTERRA EQUATION WITH NON-LIPSCHITZ COEFFICIENTS[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 872 -882 . DOI: 10.1016/S0252-9602(13)60047-8

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