摘要：For nonlinear stochastic equations d x ( t ) = [ A x ( t ) + f ( t , x ( t ) , λ ) ] d t + g ( t , x ( t ) , λ ) d ω ( t ) with parameter λ in a Hilbert space, we show the existence and uniqueness of mild solutions. Provided that f satisfies a locally Lipschitz condition and g is a uniformly Lipschitz function, some sufficient conditions for p ( p ≥ 2 ) moment locally exponential stability as well as almost surely exponential stability of mild solutions are obtained under a sufficiently small initial value ξ. Meanwhile, we also consider parameter dependence of stable mild solutions for the stochastic system if f, g are sufficiently small Lipschitz perturbations in the parameter λ.
