Acta mathematica scientia,Series B ›› 1993, Vol. 13 ›› Issue (4): 384-390.
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Xu Minghao1, Hu Zecheng2
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Abstract: 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)=y0where 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].
Xu Minghao, Hu Zecheng. UNIQUENESS OF THE MILD SOLUTION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATION IN HILBERT SPACE[J].Acta mathematica scientia,Series B, 1993, 13(4): 384-390.
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