Remarkable asymmetric random walks

Mattner, L.

doi:10.1090/S0002-9939-99-04753-X

Remarkable asymmetric random walks
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by L. Mattner

Proc. Amer. Math. Soc. 127 (1999), 1847-1854

DOI: https://doi.org/10.1090/S0002-9939-99-04753-X

Published electronically: February 17, 1999

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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.

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