随机发展方程适度解的一些性质

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 许明浩 Xu Minghao 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 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（* ） 随机发展方程 强解 适度解 stochastic evolution equation strong solution mild solution O211.63 国家自然科学基金(61672102) 1994-02-01 2021-04-01 2