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UNIQUENESS OF THE MILD SOLUTION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATION IN HILBERT SPACE
Xu Minghao, Hu Zecheng
Acta mathematica scientia,Series B. 1993, 13 (4):
384-390.
In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: dy(t)=[Ay(t)+f(t,y(t))]dt+G(t,y(t))dW(t) y(0)=y0 where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y,f(t, y):[0, T]×Y→Y, and G(t, y):[0, T]×Y→L(H, Y), y0:Ω→Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in[4].
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