Stochastic Differential Equations with Non-Lipschitz Coefficients in Hilbert Spaces |
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Authors: | Bin Xie |
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Institution: | 1. Graduate School of Mathematical Sciences , University of Tokyo , Komaba, Tokyo, Japan bxie05@sohu.com bxie@ms.u-tokyo.ac.jp |
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Abstract: | Abstract In this article, we discuss the successive approximations problem for the solutions of the semilinear stochastic differential equations in Hilbert spaces with cylindrical Wiener processes under some conditions which are weaker than the Lipschitz one. We establish the existence and the uniqueness of the solution and additionally, in our framework we consider a limiting problem for the mild solution. It is shown that the mild solution tends to the solution of the stochastic differential equation of Itô type in finite dimensional space. |
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Keywords: | Cylindrical Wiener process Limiting problem Mild solution Space-time white noise Stochastic differential equation |
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