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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

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✦ 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