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• W2165655687 abstract "Let X 1, . . . ,X N denote N independent d-dimensional Levy processes, and consider the N-parameter random field $$mathfrak{X}(t) := X_1(t_1)+cdots+ X_N(t_N).$$ First we demonstrate that for all nonrandom Borel sets $${Fsubseteq{{bf R}^d}}$$ , the Minkowski sum $${mathfrak{X}({{bf R}^{N}_{+}})oplus F}$$ , of the range $${mathfrak{X}({{bf R}^{N}_{+}})}$$ of $${mathfrak{X}}$$ with F, can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earlier joint effort with Yuquan Zhong by removing a certain condition of symmetry in Khoshnevisan et al. (Ann Probab 31(2):1097–1141, 2003). Moreover, we show that under mild regularity conditions, our necessary and sufficient condition can be recast in terms of one-potential densities. This rests on developing results in classical (non-probabilistic) harmonic analysis that might be of independent interest. As was shown in Khoshnevisan et al. (Ann Probab 31(2):1097–1141, 2003), the potential theory of the type studied here has a large number of consequences in the theory of Levy processes. Presently, we highlight a few new consequences." @default.
• W2165655687 created "2016-06-24" @default.
• W2165655687 creator A5040696011 @default.
• W2165655687 creator A5079790702 @default.
• W2165655687 date "2008-08-22" @default.
• W2165655687 modified "2023-09-26" @default.
• W2165655687 title "Harmonic analysis of additive Lévy processes" @default.
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• W2165655687 doi "https://doi.org/10.1007/s00440-008-0175-5" @default.
• W2165655687 hasPublicationYear "2008" @default.
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