Geodesic
A~limit theorem for $p$-adic-valued probability distributions
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 647-662

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Probability models in which probabilities, defined in the sense of von Mises as limits of relative frequencies, can belong to $p$-adic number fields appeared in connection with the problem of the probabilistic interpretation of wave functions in $p$-adic-valued quantum mechanics and field theory. Here we present a variant of axiomatic $p$-adic probability theory in the framework of the theory of analytic distributions on $p$-adic spaces. We prove a theorem on the existence of $p$-adic-valued probability distributions on $p$-adic sequences and obtain a limit theorem for sums of independent random variables (an analogue of the law of large numbers). 
@article{IM2_1995_59_3_a7,
     author = {A. Yu. Khrennikov},
     title = {A~limit theorem for $p$-adic-valued probability distributions},
     journal = {Izvestiya. Mathematics },
     pages = {647--662},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a7/}
}
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A. Yu. Khrennikov. A~limit theorem for $p$-adic-valued probability distributions. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 647-662. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a7/