On (c,p)-pseudostable Random Variables

J. K. Misiewicz () and G. Mazurkiewicz ()
Additional contact information
J. K. Misiewicz: University of Zielona Góra
G. Mazurkiewicz: University of Zielona Góra

Journal of Theoretical Probability, 2005, vol. 18, issue 4, 837-852

Abstract: In (Oleszkiewicz, Lecture Notes in Math. 1807), K. Oleszkiewicz defined a p-pseudostable random variable X as a symmetric random variable for which the following equation holds: $$\forall a,b \in \ IR \ \exists\ d(a,b)\ aX + bX^{\prime} \mathop{=}^{d} (|a|^p + |b|^p)^{1/p} X + d(a,b) G,$$ where G independent of X has normal distribution N(0,1), X′ denotes independent copy of X, and $$\mathop{=}^{\!\!\!\!d}$$ denotes equality of distributions. In this paper we define and study pseudostable random variables X for which the following equation holds: $$\forall a,b \in \ IR\ \exists d(a,b)\geq 0 \ aX + bX' \mathop{=}^{d} c(a,b) X + d(a,b) G_p,$$ where c is a quasi-norm on IR, G p independent of X is symmetric p-stable with the characteristic function e−|t|^p. This is a very natural generalization of the idea of p-pseudostable variables. In this notation X is p-pseudostable iff X is $$(\| \cdot \|_p, 2)$$ -pseudostable. In the paper we show that if X is (c,p)-pseudostable then there exists r>0, C, D ≥ 0 such that c(a,b) r =|a| r +|b| r and Ee e itX =exp{− C |t| p − D |t| r }.

Keywords: Symmetric stable distribution; p-pseudostable variable; functional equation; multiplicatively periodic function. (search for similar items in EconPapers)
Date: 2005
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-005-7528-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:18:y:2005:i:4:d:10.1007_s10959-005-7528-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-005-7528-0

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().