Geodesic
On probability distributions on the field of $p$-adic numbers
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 189-192

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It is shown that many naturally defined probability distributions can be realized as distributions on the field of $p$-adic numbers. Following R. Mises and E. Tornier we consider first the stochastic experiment whose elementary outcome is the result of the infinite sequence of tossings of a symmetric coin. It is proved that the distribution corresponding to this experiment is the Haar distribution on the ring of $p$-adic integers. Then we consider the convergence of series of random variables with rational values on the field of $p$-adic numbers. It is shown that the series converge a.s. on the field of $p$-adic numbers but diverge on the field of real numbers.
Mots-clés : Tornier distribution
Keywords: $p$-adic numbers, Haar distribution. 
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     author = {A. Yu. Khrennikov},
     title = {On probability distributions on the field of $p$-adic numbers},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a14/}
}
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A. Yu. Khrennikov. On probability distributions on the field of $p$-adic numbers. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 189-192. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a14/