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

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.