On the Space of BV Functions and a Related Stochastic Calculus in Infinite Dimensions

✍ Scribed by Masatoshi Fukushima; Masanori Hino

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 206 KB
• Volume: 183
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3738

✦ Synopsis

dedicated to professor leonard gross on the occasion of his 70th birthday Functions of bounded variation (BV functions) are defined on an abstract Wiener space (E, H, +) 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) 1Â2 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, 1 . Moreover, some stochastic formulae related to BV functions are investigated.