Journal of the Mathematical Society of Japan

Penalising symmetric stable Lévy paths

Kouji YANO, Yuko YANO, and Marc YOR

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Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable Lévy process of index $1 < \alpha \le 2$. The first kind is a function of the local time at the origin, and the second kind is the exponential of an occupation time integral. Special emphasis is put on the role played by a stable Lévy counterpart of the universal $\sigma $-finite measure, found in [9] and [10], which unifies the corresponding limit theorems in the Brownian setup for which $\alpha = 2$.

Article information

J. Math. Soc. Japan Volume 61, Number 3 (2009), 757-798.

First available in Project Euclid: 30 July 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 60B10: Convergence of probability measures
Secondary: 60G52: Stable processes 60G44: Martingales with continuous parameter

penalization stable process local time excursion measure


YANO, Kouji; YANO, Yuko; YOR, Marc. Penalising symmetric stable Lévy paths. J. Math. Soc. Japan 61 (2009), no. 3, 757--798. doi:10.2969/jmsj/06130757.

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