在Lipschitz条件下随机脉冲随机微分方程解的存在性和唯一性
Existence and Uniqueness of Solutions to Stochastic Differential Equations with Random Impulses under Lipschitz Conditions
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摘要: 随机脉冲随机微分方程有着广泛的应用, 本文主要研究在均方条件下, 此类方程解的存在性和唯一性. 在方程系数满足利普希兹条件以及脉冲时刻和脉冲函数满足一定条件下, 采用皮尔逊迭代, 柯系--施瓦兹不等式, 等矩公式以及随机分析中的技巧推导出结论.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.