On the uniform convergence of random series in Skorohod space and representations of càdlàg infinitely divisible processes

DOI10.1214/12-AOP783zbMath1287.60055arXiv1111.1682MaRDI QIDQ2434918

Jan Rosiński, Andreas Basse-O'Connor

Publication date: 31 January 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1682

zbMATH Keywords

series representationsstable processesinfinitely divisible processesSkorohod spaceItō-Nisio theorem

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Sample path properties (60G17) Stable stochastic processes (60G52)

Related Items (15)

Representations and isomorphism identities for infinitely divisible processes ⋮ Well-posedness of stochastic 2D hydrodynamics type systems with multiplicative Lévy noises ⋮ On infinitely divisible semimartingales ⋮ Time regularity of generalized Ornstein-Uhlenbeck processes with Lévy noises in Hilbert spaces ⋮ Functional regular variation of Lévy-driven multivariate mixed moving average processes ⋮ Stable Lévy motion with values in the Skorokhod space: construction and approximation ⋮ Almost sure uniform convergence of stochastic processes in the dual of a nuclear space ⋮ Well-posedness and large deviations for 2D stochastic Navier-Stokes equations with jumps ⋮ Numerical aspects of shot noise representation of infinitely divisible laws and related processes ⋮ From infinite urn schemes to self-similar stable processes ⋮ A general approach to sample path generation of infinitely divisible processes via shot noise representation ⋮ Polar decomposition of scale-homogeneous measures with application to Lévy measures of strictly stable laws ⋮ Time regularity of Lévy-type evolution in Hilbert spaces and of some \(\alpha \)-stable processes ⋮ Series Representation of Time-Stable Stochastic Processes ⋮ Convergence to Stable Laws in the SpaceD

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