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Generalized Lévy stochastic areas and selfdecomposability

✍ Scribed by Zbigniew J. Jurek

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
243 KB
Volume
64
Category
Article
ISSN
0167-7152

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✦ Synopsis

We show that a conditional characteristic function of generalized LÃ evy stochastic areas can be viewed as a product a selfdecomposable distribution (i.e., LÃ evy class L distribution) and its background driving characteristic function. This provides a stochastic interpretation for a ratio of some Bessel functions as well as examples of characteristic functions from van Dantzig class.

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Lévy's Stochastic Area and the Principle
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✍ Setsuo Taniguchi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 125 KB

Let (W 0 , H 0 , + 0 ) be the 2-dimensional classical pinned Wiener space over [0, 1]. A localization phenomenon will be shown for stochastic oscillatory integrals with Le vy's stochastic area as phase function.