منابع مشابه
Level Sets of Additive Lévy Processes
We provide a probabilistic interpretation of a class of natural capacities on Euclidean space in terms of the level sets of a suitably chosen multiparameter additive Lévy process X . We also present several probabilistic applications of the aforementioned potential-theoretic connections. They include areas such as intersections of Lévy processes and level sets, as well as Hausdorff dimension co...
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Different extensions of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Lévy processes; n-fold “near-intersections” of a single Lévy process and continuous additive functionals of several independent Lévy processes. Intersection local times for n independent Lévy processes are also studied. They are related to both of the ...
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X(n) = X1(n1) + · · ·+XN (nN ), n ∈ N0 . Here, nj denotes the jth coordinate of n ∈ N0 . We are following the standard convention of starting (ordinary) random walks at the origin. That is, Xj(0) = 0 for all j = 1, . . . , N . From now on, N will always denote the temporal dimension and d the spatial one, to use the standard language of stochastic processes. In order to describe a natural parti...
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This is Theorem 1.1 of Khoshnevisan, Xiao and Zhong [1] with no assumptions. If we let X = 0 we obtain Theorem 2.1 of Khoshnevisan, Xiao and Zhong [1]. If we take a standard additive α-stable process Sα from IR+ to IR d with α ∈ (0, 1) to be X, we obtain Theorem 2.2 of Khoshnevisan and Xiao [2]. If we consider a deterministic additive Lévy process from IR+ to IR d as Y , we obtain For any F ∈ B...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2002
ISSN: 0091-1798
DOI: 10.1214/aop/1020107761