𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Sard Inequality on Wiener Space

✍ Scribed by A.S. Üstünel; M. Zakai

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
355 KB
Volume
149
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

Let T(w)=w+u(w) be a Cameron Martin perturbation of the identity. The formal infinite dimensional extension of the Sard inequality,

is shown to hold and applications to absolute continuity on Wiener space are presented.

1997 Academic Press

I. INTRODUCTION

The Sard lemma on

then the Lebesgue measure of E 0 is zero. This result is useful in many applications as it often avoids the need to consider what happens on E 0 . In [9], J. T. Schwartz presented a generalization of this result: Theorem 1.1 [9]. Let D and T be as above and let J(x) denote the Jacobian determinant of T at x; also, let E be a measurable subset of D, then T(E) is measurable and

📜 SIMILAR VOLUMES

Tangent Processes on Wiener Space
Tangent Processes on Wiener Space
✍ Y. Hu; A.S. Üstünel; M. Zakai 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 274 KB

This paper deals with the study of the Malliavin calculus of Euclidean motions on Wiener space (i.e. transformations induced by general measure-preserving transformations, called ''rotations'', and H -valued shifts) and the associated flows on abstract Wiener spaces.

Analytic Functions on Abstract Wiener Sp
Analytic Functions on Abstract Wiener Spaces
✍ Setsuo Taniguchi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 181 KB

dedicated to professor d. w. stroock on his 60th birthday Let (X, H, +) be a real abstract Wiener space. A new definition of analytic functions on X is introduced, and it is shown that stochastic line integrals of real analytic 1-forms along Brownian motion and solutions to stochastic differential e

Flows Associated to Tangent Processes on
Flows Associated to Tangent Processes on the Wiener Space
✍ Fernanda Cipriano; Ana Bela Cruzeiro 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 174 KB

We prove, under certain regularity assumptions on the coefficients, that tangent processes (namely semimartingales d! { =a dx { +b d{ where a is an antisymmetric matrix) generate flows on the classical Wiener space. Main applications of the result can be found in the study of the geometry of path sp

On the Davis inequality in Banach functi
On the Davis inequality in Banach function spaces
✍ Masato Kikuchi 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 172 KB 👁 1 views

## Abstract We give a characterization of those Banach function spaces in which the Davis inequality for martingales is valid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)