On stochastic processes associated with relativistic stable distributions
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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.
KeywordsLévy 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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