✦ LIBER ✦
Substitution to parametrized generalized Wiener functionals and pinned Brownian local times
✍ Scribed by Hideaki Uemura
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- French
- Weight
- 152 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0007-4497
No coin nor oath required. For personal study only.
✦ Synopsis
We discuss how to substitute Wiener functionals for parameters in generalized Wiener functionals: Let {Φ(x); x ∈ R N } be generalized Wiener functionals parametrized by x ∈ R N and F be a non-degenerate Wiener functional in Malliavin's sense. Then, formally, it holds that Φ(F ) = R N Φ(x)δ x (F ) dx. We define the substitution by justification of the formal representation above. Under this definition we show the relationship between pinned Brownian local times and Brownian local times. 2001 Éditions scientifiques et médicales Elsevier SAS