2009 Volume 61 Issue 3 Pages 757-798
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<α≤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 σ-finite measure, found in [9] and [10], which unifies the corresponding limit theorems in the Brownian setup for which α=2.
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