Infinite-dimensional degree theory and stochastic analysis
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 1661-7738Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s11784-010-0009-9
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|
|Official Date:||June 2010|
|Number of Pages:||33|
|Page Range:||pp. 33-65|
|Access rights to Published version:||Restricted or Subscription Access|
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