Remarkable asymmetric random walks
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Abstract:
There exists an asymmetric probability measure $P$ on the real line with $P^{\ast n} (]0,\infty [) + (1/2) P^{\ast n} (\{0\}) = 1/2$ 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
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Additional Information
- L. Mattner
- Affiliation: Universität Hamburg, Institut für Mathematische Stochastik, Bundesstr. 55, D–20146 Hamburg, Germany
- MR Author ID: 315405
- Email: mattner@math.uni-hamburg.de
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1847-1854
- MSC (1991): Primary 60J15, 60E10, 62E10, 62G05
- DOI: https://doi.org/10.1090/S0002-9939-99-04753-X
- MathSciNet review: 1487326