Stochastic Cauchy Problem in UMD Banach Spaces

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Ghasempour, Mohammad | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48129 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohuri Zangeneh, Bijan
Abstract:
We discuss, in the setting of UMD Banach spaces E, existence, uniqueness and the continuous dependence on the data A, F, G and of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t;X(t))]dt + G(t;X(t))dWH(t); t 2 [0; T]; X(0) = ; Where A generates an analytic C0-semigroup on a UMD Banach space E and WH is a cylindrical Brownian motion with values in a Hilbert space H. We can see that if the mappings F : [0; T] E ! E and G : [0; T] E ! L(H;E) satisfy suitable Lipschitz conditions and is F0-measurable and bounded, then this problem has a unique mild solution.And We arw going to review continuous dependence of the solutions X(t), assuming that the approximating operators An are uniformly sectorial and converge to A in the strong resolvent sense and that the approximating nonlinearities Fn and Gn are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise
Keywords:
Uniqueness ; Existence ; Banach Spaces ; Stochastic Evolution Equation ; Unconditional Martingale Differences (UMD)Banach Space ; Semilinear Stochastic Evolution Equation ; Solution Continous Dependence ; Lipschitz Continuous