Additive Lévy Processes
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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...
متن کاملModerate Deviations and Laws of the Iterated Logarithm for the Local times of Additive Lévy Processes and Additive Random Walks
We study the upper tail behaviors of the local times of the additive Lévy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L2-norms of the local times and for the local times at a fixed site. Subject classifications: 60F10, 60F15, 60J55, 60G52
متن کاملAdditive Lévy Processes: Capacity and Hausdorff Dimension
This is a survey on recently-developed potential theory of additive Lévy processes and its applications to fractal geometry of Lévy processes. Additive Lévy processes arise naturally in the studies of the Brownian sheet, intersections of Lévy processes and so on. We first summarize some recent results on the novel connections between an additive Lévy process X in R , and a natural class of ener...
متن کاملAdditive functionals of several Lévy processes and self-intersection local times
Different extentons 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, which is also referred to as a self-intersection local time, and continuous additive functionals of several independent Lévy processes. Intersection local times for n independent Lévy...
متن کاملLocal Times of Additive Lévy Processes
Let X = {X(t); t ∈ R+} be an additive Lévy process in R with X(t) = X1(t1) + · · ·+ XN (tN ), ∀t ∈ R+ , where X1, · · · , XN are independent, classical Lévy processes on R with Lévy exponents Ψ1, . . . , ΨN respectively. Under mild regularity conditions on the Ψi’s, we derive moment estimates that imply joint continuity of the local times in question. These results are then refined to precise e...
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تاریخ انتشار 2011