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- W1569437656 abstract "The thesis deals with various aspects of the study of stochastic partial differential equations driven by Gaussian noise. The approach taken is functional analytic rather than probabilistic: the stochastic partial differential equation is interpreted as an ordinary stochastic differential equation in a Banach space. The major part of the thesis deals with approximations of solutions to semi-linear stochastic differential equations. We consider discretizations both in time and in space. We prove optimal convergence rates for pathwise convergence of the implicit-linear Euler scheme. Concerning space approximations, we first prove a perturbation result, which allows us to obtain pathwise convergence of certain Galerkin and finite element schemes in the Hilbert space case. Because we obtain pathwise convergence, we can allow for the non-linearities to be locally Lipschitz instead of globally Lipschitz. Apart from the results on approximations, the thesis also contains a part in which we prove existence and uniqueness of solutions to a rather general class of stochastic delay equations. Finally, there is a part on decoupling, which is a concept that plays a role when defining the stochastic integral of a stochastic process taking values in a Banach space." @default.
- W1569437656 created "2016-06-24" @default.
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- W1569437656 date "2012-03-12" @default.
- W1569437656 modified "2023-09-26" @default.
- W1569437656 title "Stochastic Differential Equations in Banach Spaces: Decoupling, Delay Equations, and Approximations in Space and Time" @default.
- W1569437656 hasPublicationYear "2012" @default.
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