Penalising symmetric stable Lévy paths
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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 < α\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 $ σ$-finite measure, found in [9] and [10], which unifies the corresponding limit theorems in the Brownian setup for which $ α=2 $.
33 pages
33 pages