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A note on random walks in multidimensional time

Published online by Cambridge University Press:  24 October 2008

Janos Galambos  and
Imre Kátai
Janos Galambos
Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A.
Imre Kátai
Affiliation:
Institute of Mathematics, L. Eötvös University, Budapest 1088, Hungary
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Extract

Let Kr denote the set of r-tuples n = (n1, n2, …, nr), r ≥ 1, where the components ni are positive integers. Let {X, Xn, n ∈ Kr} be a family of independent and identically distributed random variables with positive mean EX = μ < + ∞ and finite variance VX = σ2 < + ∞. In a recent work, M. Maejima and T. Mori [2] have shown that, if X is integer valued, aperiodic and E∣X∣3 < + ∞, then, for r = 2 or 3,

where

the summation being extended over all members j = (j1,j2, …, jr) of Kr that satisfy jt ≤ nt for all 1 ≤ t ≤ r.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 163 - 170
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

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