Stochastic integration in Banach spaces – a survey. (English) Zbl 1333.60115
Dalang, Robert C. (ed.) et al., Stochastic analysis: a series of lectures. Centre Interfacultaire Bernoulli, January–June 2012, École Polytechnique Fédérale Lausanne, Switzerland. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0908-5/hbk; 978-3-0348-0909-2/ebook). Progress in Probability 68, 297-332 (2015).
Summary: This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are presented, as well as some applications of the latter to vector-valued Malliavin calculus and the stochastic maximal regularity problem. A new proof of the stochastic maximal regularity theorem is included.
For the entire collection see [Zbl 1330.60004].
For the entire collection see [Zbl 1330.60004].
MSC:
60H05 | Stochastic integrals |
60H07 | Stochastic calculus of variations and the Malliavin calculus |
60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
46B09 | Probabilistic methods in Banach space theory |
46E40 | Spaces of vector- and operator-valued functions |
60B11 | Probability theory on linear topological spaces |
60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |
Keywords:
stochastic integration; UMD Banach spaces; martingale type; \(\gamma\)-radonifying operators; Malliavin calculus; \(R\)-boundedness; stochastic maximal regularityReferences:
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.