On the space of BV functions and a related stochastic calculus in infinite dimensions

被引：54

作者：

Fukushima, M ^{[1
]}

Hino, M

机构：

[1] Kansai Univ, Fac Engn, Dept Math, Suita, Osaka 5648680, Japan

[2] Kyoto Univ, Grad Sch Informat, Dept Appl Anal & Complex Dynam Syst, Kyoto 6068501, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2001年 / 183卷 / 01期

关键词：

BV function; abstract Wiener space; Orlicz space; surface measure; Dirichlet form; distorted Ornstein-Uhlenbeck process; generalized Ito's formula;

D O I：

10.1006/jfan.2000.3738

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Functions of bounded variation (BV functions) are defined on an abstract Wiener space (E, H,mu) in a way similar to that in finite dimensions. Some characterizations are given, which justify describing a BV function as a function in L(log L)(1/2) with the first order derivative being an H-valued measure. It is also shown that the space of BV functions is obtained by a natural extension of the Sobolev space D-1,D-1. Moreover, some stochastic formulae related to BV functions are investigated. (C) 2001 Academic Press.

引用

页码：245 / 268

页数：24

共 29 条

[1] LOGARITHMIC SOBOLEV INEQUALITIES AND EXPONENTIAL INTEGRABILITY [J].

AIDA, S ;

MASUDA, T ;

SHIGEKAWA, I .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 126 (01) :83-101

[2]

AIRAULT H, 1988, B SCI MATH, V112, P3

[3]

[Anonymous], ACTA MATH U CAROLINA

[4]

[Anonymous], FUNCTIONS BOUNDED VA

[5]

[Anonymous], LECT NOTES MATH

[6]

Bogachev V. I., 1998, Gaussian Measures

[7]

Bouleau N., 1991, DIRICHLET FORMS ANAL, V14

[8] RADEMACHERS THEOREM FOR WIENER FUNCTIONALS [J].

ENCHEV, O ;

STROOCK, DW .

ANNALS OF PROBABILITY, 1993, 21 (01) :25-33

[9]

Evans L. C., 2018, Measure Theory and Fine Properties of Functions

[10]

Federer H., 1969, GEOMETRIC MEASURE TH

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