Print Email Facebook Twitter Stochastic Differential Equations in Banach Spaces: Decoupling, Delay Equations, and Approximations in Space and Time Title Stochastic Differential Equations in Banach Spaces: Decoupling, Delay Equations, and Approximations in Space and Time Author Cox, S.G. Contributor Van Neerven, J.M.A.M. (promotor) Faculty Electrical Engineering, Mathematics and Computer Science Department Applied mathematics Date 2012-03-12 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. Subject Stochastic partial differential equations To reference this document use: http://resolver.tudelft.nl/uuid:8bd83f5a-e995-42c2-b237-a9fa3a084578 ISBN 9789461860224 Part of collection Institutional Repository Document type doctoral thesis Rights (c) 2012 Cox, S.G. Files PDF ThesisSonja_repository_notags.pdf 1.09 MB Close viewer /islandora/object/uuid:8bd83f5a-e995-42c2-b237-a9fa3a084578/datastream/OBJ/view