Infinite-dimensional degree theory and stochastic analysis

被引：1

作者：

Al-Hussein, A. ^{[1
]}

Elworthy, K. D. ^{[2
]}

机构：

[1] Qassim Univ, Coll Sci, Dept Math, Buraydah 51452, Saudi Arabia

[2] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2010年 / 7卷 / 01期

关键词：

Abstract Wiener space; degree; Leray-Schauder; Sard's theorem; Fredholm map; Banach manifold; Fredholm structure; pull-back measures; diiffeomorphism group; McKean-Singer formula; Rice formula; Malliavin calculus; BANACH MANIFOLDS; FREDHOLM MAPS; WIENER-SPACES; EQUATIONS;

D O I：

10.1007/s11784-010-0009-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：33 / 65

页数：33

共 60 条

[51]

Schwartz J., 1969, NONLINEAR FUNCTIONAL

[52]

Schwartz L., 1973, Tata Inst. Fund. Res. Stud. Math., V6

[53] AN INFINITE DIMENSIONAL VERSION OF SARDS THEOREM [J].