Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations |
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| Authors: | Mark C Veraar |
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| Institution: | 1. Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands
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| Abstract: | In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E: $({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in 0,T], \\ U(0) = u_0.\end{array}\right.$ Here, ${(A(t))_{t\in 0,T]}}In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E:
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(SE) {ll dU(t) = (A(t)U(t) +F(t,U(t))) dt + B(t,U(t)) dWH(t), t ? 0,T], U(0) = u0.({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in 0,T], \\ U(0) = u_0.\end{array}\right. |
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