Regard the stochastic differential delay equation dx(t)=[(A+Ā(t))x(t)+(B+B̄(t− τ)) x(t−τ)]dt+g(t,x(t),x(t−τ))dw(t) as the result of the effects of uncertainty, stochastic perturbation and time lag to a linear ordinary differential equation ẋ(t)=(A+B)x(t). Assume the linear system is exponentially stable. In this paper we shall characterize how much the uncertainty, stochastic perturbation and ti...

In this paper we consider a class of {\it conditional McKean-Vlasov SDEs} (CMVSDE for short). Such an SDE can be considered as extended version SDEs with common noises, well the general so-called mean-field (CMFSDE) studied previously by authors [1, 14], but some fundamental differences. particular, due to lack compactness iterated laws, existing arguments Schauder's fixed point theorem do not ...