Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 61, Number 3 (2009), 757-798.
Penalising symmetric stable Lévy paths
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  and , which unifies the corresponding limit theorems in the Brownian setup for which $\alpha = 2$.
J. Math. Soc. Japan Volume 61, Number 3 (2009), 757-798.
First available in Project Euclid: 30 July 2009
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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. https://projecteuclid.org/euclid.jmsj/1248961478.