In this article, we propose two types of explicit tamed Euler–Maruyama (EM) schemes for neutral stochastic differential delay equations with superlinearly growing drift and diffusion coefficients. The first type is convergent in the Lq sense under local Lipschitz plus Khasminskii-type conditions. second order half mean-square Khasminskii-type, global monotonicity polynomial growth Moreover, it ...

This paper is devoted to the convergence analysis of stochastic θ-methods for nonlinear neutral stochastic differential delay equations (NSDDEs) in Itô sense. The basic idea is to reformulate the original problem eliminating the dependence on the differentiation of the solution in the past values, which leads to a stochastic differential algebraic system. Drift-implicit stochastic θ-methods are...

Neutral delay differential equations contain the derivative of the unknown function both with and without delays. Some new phenomena can appear, hence the theory of neutral delay differential equations is even more complicated than the theory of non-neutral delay equations. The oscillatory behavior of the solutions of neutral systems is of importance in both the theory and applications, such as...

This article aims to mark out new conditions for oscillation of the even-order Emden–Fowler neutral delay differential equations with term ?1???[?r?1?]?+?3???[???]=0. The obtained results extend, and simplify known in literature. are illustrated examples.

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we p...