A survey of change of scale formulas on an analogue of Wiener space. (English) Zbl 1381.28014
Dang, Pei (ed.) et al., New trends in analysis and interdisciplinary applications. Selected contributions of the 10th ISAAC congress, Macau, China, August 3–8, 2015. Basel: Birkhäuser/Springer (ISBN 978-3-319-48810-3/pbk; 978-3-319-48812-7/ebook). Trends in Mathematics. Research Perspectives, 355-361 (2017).
Summary: Let \((C[0, t], w_\varphi)\) denote an analogue of Wiener space, that is, the space of real-valued continuous paths on \([0, t]\). The measure \(w_{\varphi}\) and \(w_{\varphi}\)-measurability behave badly under change of scale, and under translation. In this paper we introduce several change of scale formulas on \(C[0, t]\) for the generalized analytic conditional Wiener integrals of the cylinder functions and the functions in a Banach algebra which corresponds to the Cameron-Storvick’s Banach algebra.
For the entire collection see [Zbl 1371.26002].
For the entire collection see [Zbl 1371.26002].
MSC:
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 60G05 | Foundations of stochastic processes |
