CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2010, 26(4) 347-356 DOI:      ISSN: 1001-4268 CN: 31-1256

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Existence and Uniqueness of Solutions to Stochastic Differential Equations with Random Impulses under Lipschitz Conditions

Zhou Yong,Wu Shujin

Department of Statistics and Acruarial Science,East China Normal University

Abstract��

Stochastic differential equations with
random impulses should have extensive applications. In this paper,
the existence and uniqueness in mean square of solutions to these
equations are considered. To achieve the desired results, many
techniques are used, such as Pearson iteration, the Cauchy-Schwarz
inequality, Lipschitz conditions, Ito isometry, martingale
inequality and some stochastic analysis.

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