Pathwise Estimation of Stochastic Differential Equations with Unbounded Delay and Its Application to Stochastic Pantograph Equations

Authors:
Xuejing Meng;Shigeng Hu;Ping Wu
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China 430074;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China 430074;Department of the Basics, Air Force Radar Academy, Wuhan, P.R. China 430019
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2011

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Abstract

The existence and uniqueness of the global solution of stochastic differential equations with discrete variable delay is investigated in this paper, and the pathwise estimation is also done by using Lyapunov function method and exponential martingale inequality. The results can be used not only in the case of bounded delay but also in the case of unbounded delay. As the applications, this paper considers the pathwise estimation of solutions of stochastic pantograph equations.