Allameh Tabataba'i University Press Journal of Mathematics and Modeling in Finance 2783-0578 1 1 2021 03 01 Mean-square stability and convergence of compensated split-step θ-method for nonlinear jump diffusion systems 83 101 11917 10.22054/jmmf.2020.54500.1011 EN Ali R. Soheili Department of applied mathematics Ferdowsi university of Mashhad Mashhad, Iran Yasser Taherinasab Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran Mohammad Amini Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Journal Article 2020 08 13 In this paper, the existence and uniqueness of the numerical solution of the Stochastic Differential Equations with Jumps(SDEwJs) under the one side Lipschitz conditions and polynomial growth conditions are presented. The Compensated split step θ(CSSθ) method introduce and try to bound the moment of the numerical solutions also we analyse the strong convergence on the compact domain. We discuss the stability of SDEwJs with constant coefficient and prove some new relation between their coefficient. Finally, we present three examples to investigate the theories and methods. nonlinear stochastic differential equations Poisson jump compensated split-step ‎$theta‎$ method one-sided Lipschitz condition forward-backward Euler-Maruyama method mean-square stability https://jmmf.atu.ac.ir/article_11917_c9eed04eaeb25d7e4ad8f29255a807db.pdf