Lévy processes and stochastic integrals in the sense of generalized convolutions

DOI10.3150/14-BEJ653zbMath1333.60091arXiv1312.4083OpenAlexW2125429514MaRDI QIDQ888492

Jan Rosiński, Jolanta K. Misiewicz, Barbara H. Jasiulis-Gołdyn, Marta Borowiecka-Olszewska

Publication date: 30 October 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4083

zbMATH Keywords

Lévy processesinfinitely divisible distributionsstochastic integralssymmetric stable distributionrandom measuresgeneralized convolutionsweakly stable distribution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Stochastic integrals (60H05) Random measures (60G57)

Related Items (11)

Renewal theory for extremal Markov sequences of Kendall type ⋮ Cramér-Lundberg model for some classes of extremal Markov sequences ⋮ Asymptotic properties of extremal Markov processes driven by Kendall convolution ⋮ How exceptional is the extremal Kendall and Kendall-type convolution ⋮ Slash distributions, generalized convolutions, and extremes ⋮ Classical definitions of the Poisson process do not coincide in the case of generalized convolutions ⋮ Lévy process with substable increments via generalized convolution ⋮ Kendall random walk, Williamson transform, and the corresponding Wiener-Hopf factorization ⋮ Generalized convolutions and the Levi-Civita functional equation ⋮ A unified construction of product formulas and convolutions for Sturm-Liouville operators ⋮ Lévy processes with respect to the Whittaker convolution

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