On Weak Generalized Stability and (c,d)-Pseudostable Random Variables via Functional Equations |
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Authors: | W Jarczyk J K Misiewicz |
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Institution: | (1) Department of Mathematics Informatics and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65-516 Zielona Góra, Poland |
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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.
This paper was partially written while the second author was a visiting professor of Delft Institute of Applied Mathematics,
Delft University of Technology, Holland. |
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Keywords: | Weakly stable distribution Symmetric stable distribution ℓ α -symmetric distribution Generalized convolution Scale mixture Functional equation Convexity |
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