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Remarkable asymmetric random walks

Author: L. Mattner
Journal: Proc. Amer. Math. Soc. 127 (1999), 1847-1854
MSC (1991): Primary 60J15, 60E10, 62E10, 62G05
Published electronically: February 17, 1999
MathSciNet review: 1487326
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Abstract: There exists an asymmetric probability measure $P$ on the real line with $P^{\ast n} (]0,\infty[) + (1/2) P^{\ast n} ({\left\{ 0 \right\}}) = 1/2$ for every $n \in \mathbf{N}$. $P$ can be chosen absolutely continuous and $P$ can be chosen to be concentrated on the integers. In both cases, $P$ can be chosen to have moments of every order, but $P$ cannot be determined by its moments.

References [Enhancements On Off] (What's this?)

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Additional Information

L. Mattner
Affiliation: Universität Hamburg, Institut für Mathematische Stochastik, Bundesstr. 55, D–20146 Hamburg, Germany

Keywords: Characteristic function, characterization of symmetry, Edgeworth expansion, Gurland inversion, median unbiased estimator.
Received by editor(s): May 5, 1997
Received by editor(s) in revised form: September 22, 1997
Published electronically: February 17, 1999
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1999 American Mathematical Society

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