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Infinite-dimensional degree theory and stochastic analysis
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Al-Hussein, A. and Elworthy, K. D.. (2010) Infinite-dimensional degree theory and stochastic analysis. Journal of Fixed Point Theory and Application, Vol.7 (No.1). pp. 33-65. ISSN 1661-7738
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Official URL: http://dx.doi.org/10.1007/s11784-010-0009-9
Abstract
The main aim of this paper is to describe how stochastic analysis is applied to infinite-dimensional degree theory for measurable maps of Banach spaces and Fredholm maps between Banach manifolds. It is based on work of Getzler, Kusuoka, and Ustunel & Zakai. Topics include the following: measure-theoretic versions of Sard's theorem and inequality, pull-backs of measures by Fredholm maps, integral formulae for the degree, infinite-dimensional area formulae, generalised McKean-Singer formulae for Euler characteristics, and generalised Rice formulae. Introductory material on Gaussian measures and stochastic analysis is included.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Journal of Fixed Point Theory and Application |
| Publisher: | Birkhauser Verlag AG |
| ISSN: | 1661-7738 |
| Date: | June 2010 |
| Volume: | Vol.7 |
| Number: | No.1 |
| Number of Pages: | 33 |
| Page Range: | pp. 33-65 |
| Identification Number: | 10.1007/s11784-010-0009-9 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/5775 |
Data sourced from Thomson Reuters' Web of Knowledge
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