随机发展方程适度解的一些性质

SOME PROPERTIES OF THE SOLUTION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES

研究了如下Ｈｉｌｂｅｒｔ空间中的半线性随机发展方程的Ｃａｕｃｈｙ问题的适度解ｙ（ｔ；τ，Ｚ）的性质：在所给条件下，ｙ（ｔ；τ，Ｚ）的Ｐ（Ｐ≥２）阶矩的有界性及在ｐ阶矩意义下对初值的连续相依性．同时，我们还讨论了问题的强解与适度解的关系，此处，Ｒ（λ，Ａ）是Ａ的预解式，并建立了该问题的强解与问题的适度解的联系．

In this paper,We discussed two problems:first, we discussed properties of the mild solution y(t:τ, Z)of the following Cauchy problem of semilinear stochastic evolution equations in HilbertSpacesWhere 0≤τ<t≤T, E | Z| p<∞ (p≥ 2). We obtain two useful properties on the mild solution of theproblem. Second,We proved the mild solution of the following Cauchy problemis a strong solution of the problem,Where R(λ)=λR(λ,A),R(λ, A) is the resolvent of A, λ∈ P(A),p(A)is the resolvent set of A. Together, we also establish connection of the mild solution of the following Cauchy problem with(* )