Research On Averaging Principle And Numerical Algorithm Of Two-time-scale Jump-diffusion Stochastic Systems With Non-Lipschitz Conditions

In this paper,we consider some problems for one-dimensional two-time-scale jump-diffusion systels under the non-Lipschitz conditions of Yamada-Watanabe type,including the averaging principle and numerical algorithm.The main details are as follows:Firstly,under the non-Lipscbitz conditions,we devote to proving the existence and unique-ness of solutions for two-time-scale jump-diffusion systems.Moreover,we obtain the strong averaging principle on the basis of the conclusion.Secondly,we concentrate on studying the nu-merical schemes for two-time-scale jump-diffusion systems under the non-Lipschitz conditions.At the same time,the boundedness of convergence for the approximate solutions is also shown.