Numerical Solutions of Hybrid Stochastic Differential Delay Equations under the Generalized Khasminskii-Type Conditions

The main aim of this paper is to discuss the numerical solution of nonlinear hybrid stochastic differential （SDDEs）, where the linear growth condition is replaced by the more general Khasminskii-type condition Khasminskii condition covers a wide class of highly nonlinear hybrid SDDEs whose solution is not explicit. delay equations This generalized We establish the existence-and-uniqueness theorem and prove the Euler-Maruyama approximations converge to the true solution in probability