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  • 1 Budapest University of Technology and Economics Department of Mathematics Műegyetem rkp. 3, H ép. V. em. H-1521 Budapest Hungary Műegyetem rkp. 3, H ép. V. em. H-1521 Budapest Hungary
  • 2 Budapest University of Technology and Economics Budapest Budapest
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Abstract  

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ1 + ξ1ξ2 + ξ1ξ2ξ3 + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μk = Ek) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle.