Lithuanian Mathematical Journal

, Volume 41, Issue 3, pp 239–251

Generalized z-Distributions and Related Stochastic Processes


  • B. Grigelionis
    • Institute of Mathematics and Informatics, Akademijos 4;Vilnius University

DOI: 10.1023/A:1012806529251

Cite this article as:
Grigelionis, B. Lithuanian Mathematical Journal (2001) 41: 239. doi:10.1023/A:1012806529251


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.

$z$–distributionsMeixner distributionsOrnstein–Uhlenbeck–type processEsscher transformmixed exponential processself–decomposabilityself–similarityergodic diffusion
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© Plenum Publishing Corporation 2001