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

Functions of bounded variation (BV functions) are defined on an abstract Wiener space (E, H, μ) 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 D1, 1. Moreover, some stochastic formulae related to BV functions are investigated.