Lithuanian Mathematical Journal

, Volume 48, Issue 1, pp 61–69 | Cite as

On stochastic processes associated with relativistic stable distributions

  • B. Grigelionis


Lévy processes with marginal relativistic α-stable distributions are described. Strictly stationary Ornstein-Uhlenbeck type processes with one-dimentional relativistic α-stable distributions are constructed. The exponential family as Esscher transforms of distributions on D [0,∞)(R d ) of relativistic α-stable Lévy processes is obtained and the corresponding mixed exponential processes are characterized.


Lévy process mixed exponential process Ornstein-Uhlenbeck type process relativistic α-stable distribution relativistic Schrödinger operator subordinated Gaussian Lévy process Thorin subordinator 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsVilniusLithuania

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