On Weak Generalized Stability and (c,d)-Pseudostable Random Variables via Functional Equations

W. Jarczyk () and J. K. Misiewicz ()
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W. Jarczyk: University of Zielona Góra
J. K. Misiewicz: University of Zielona Góra

Journal of Theoretical Probability, 2009, vol. 22, issue 2, 482-505

Abstract: Abstract In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution, focusing our attention on the symmetric weakly stable distribution. As in the case of the classical convolution, characterization of distributions stable in the sense of weak generalized convolution depends on solving some functional equations in the class of characteristic functions.

Keywords: Weakly stable distribution; Symmetric stable distribution; ℓ α -symmetric distribution; Generalized convolution; Scale mixture; Functional equation; Convexity; 60A10; 60B05; 60E05; 60E07; 60E10; 39B22; 26A51 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-008-0195-1

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