### Penalising symmetric stable Lévy paths

Kouji YANO, Yuko YANO, and Marc YOR
Source: J. Math. Soc. Japan Volume 61, Number 3 (2009), 757-798.

#### Abstract

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 $\alpha = 2$.

First Page:
Primary Subjects: 60B10
Secondary Subjects: 60G52, 60G44
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1248961478
Digital Object Identifier: doi:10.2969/jmsj/06130757
Mathematical Reviews number (MathSciNet): MR2552915

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