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Title
Abstract
Key Takeaways
BV Functions in the Finite-Dimensional Case
References

An introduction to $BV$ functions in Wiener spaces

Profile image of Matteo NovagaMatteo Novaga

2012, Eprint Arxiv 1212 5926

Abstract

We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.

Key takeaways
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  1. This paper establishes foundational theory for functions of bounded variation (BV) in abstract Wiener spaces.
  2. Malliavin calculus connects BV functions to stochastic differential equations and various mathematical fields.
  3. The authors present key equivalences for BV functions, critical for understanding their properties in infinite dimensions.
  4. Applications of BV theory include geometric analysis and probabilistic interpretations in stochastic processes.
  5. The text serves as an introductory resource for students and researchers in variational methods and infinite dimensional analysis.

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