Harmonic analysis of additive Lévy processes
نویسندگان
چکیده
منابع مشابه
Harmonic Analysis of Additive Lévy Processes
Let X1, . . . , XN denote N independent d-dimensional Lévy processes, and consider the N -parameter random field X(t) := X1(t1) + · · ·+XN (tN ). First we demonstrate that for all nonrandom Borel sets F ⊆ R, the Minkowski sum X(R+ ) ⊕ F , of the range X(R+ ) of X with F , can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earli...
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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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Let X1, . . . , XN denote N independent d-dimensional Lévy processes, and consider the N -parameter random field X(t) := X1(t1) + · · ·+XN (tN ). First we demonstrate that for all nonrandom Borel sets F ⊆ R, the Minkowski sum X(R+ ) ⊕ F , of the range X(R+ ) of X with F , can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earli...
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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: Probability Theory and Related Fields
سال: 2008
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-008-0175-5