Lithuanian Mathematical Journal

, Volume 41, Issue 3, pp 239-251

First online:

Generalized z-Distributions and Related Stochastic Processes

  • B. GrigelionisAffiliated withInstitute of Mathematics and Informatics, Akademijos 4;, Vilnius University

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The class of generalized z–distributions is defined and their properties are investigated. Ornstein–Uhlenbeck–type and self–similar generalized z–processes are constructed and described. Esscher transforms of the generalized z–processes and the mixed generalized z–processes are characterized. Finally, construction and some properties of generalized z–diffusions are also discussed.

$z$–distributions Meixner distributions Ornstein–Uhlenbeck–type process Esscher transform mixed exponential process self–decomposability self–similarity ergodic diffusion