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:
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