# Stochastic Evolution Equations with Adapted Drift

Stochastic Evolution Equations with Adapted Drift

Author Contributor Faculty Department Date2013-11-12

AbstractIn this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance mathematical finance and filtration theory. Second, we restrict ourselves to UMD Banach spaces with type 2. As the theory of Ito stochastic integration is insufficient for studying equations of this general type, we need to have a proper understanding of several extensions to the Ito integral. Two of such extensions that are considered rigorously in this thesis are the Skorohod integral and the forward integral. Moreover, in Chapter 5, a new solution concept is introduced. The relationship between other solution concepts is discussed. Finally, we prove existence, uniqueness and regularity of solutions to stochastic evolution equations with adapted drift.

SubjectMalliavin Calculus

Stochastic Partial Differential Equations

Stochastic Evolution Equations

Forward Integration

Truncated Skorohod Integral

Space-Time Regularity

UMD Banach space

path-wise mild solution

stochastic convolution

adapted drift

non-adapted processes

https://doi.org/10.4233/uuid:0f1c8773-f7e9-412e-b1e4-283e0cf33ee6

ISBN9789461085375

Part of collectionInstitutional Repository

Document typedoctoral thesis

Rights(c) 2013 Pronk, M.