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Asymptotics for a Curve with a Given Distribution Density of the First Exit Position for a Wiener Process

✍ Scribed by B. P. Harlamov

Book ID
110329549
Publisher
Springer US
Year
2002
Tongue
English
Weight
198 KB
Volume
109
Category
Article
ISSN
1573-8795

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## Abstract If ΞΎ(t) is the solution of homogeneous SDE in R m, and T βˆƒ is the first exit moment of the process from a small domain D βˆƒ, then the total expansion for the following functional showing independence of the exit time and exit place is $$Eexp( - \lambda T\_\varepsilon )f(\frac{{\xi (T\_\v

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Let f be an R'-valued Wiener functional, which is smooth and non-degenerate in the sense of the Malliavin calculus. Let p be the density, with respect to the Lebesgue measure on R", of its law. We are interested in the set U = {p > O}. We prove that U is connected. As a consequence, the intrinsic di