Numerical Solutions Of Nonlinear Hybrid Stochastic Differential Delay Equations Under The Generalized Khasminskii-Type Conditions

In this paper,we establish the Khasminskii-type existence and uniqueness theorem for hybrid SDDEs,where the linear growth condition is replaced by the generalized Khasminskii condition.These generalized Khasminskii condition covers a wide class of highly nonlinear hybrid SDDEs while the solution is not explicit.And we prove the Euler-Maruyama approximations converge to the true solution in probability.And then we give an illustrative sample for the numerical method.Finally,we give the conditions which guarantee the mean square stability of the Euler-Maruyama approximation.