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Teor. Veroyatnost. i Primenen., 1969, Volume 14, Issue 4, Pages 693–707 (Mi tvp1481)  

On limiting distributions for moduli of sequential differences of independent variables

S. S. Vallander, I. A. Ibragimov, N. G. Lindtrop

Leningrad

Abstract: Let $(\xi,\eta)$ be a pair of independent equally distributed random variables, and $F(x)$ be their common distribution function. We define a sequence of pairs $(\xi_n,\eta_n)$ of independent equally distributed random variables with distribution functions $F_n(x)$:
$$ F_1(x)=\mathbf\{|\xi-\eta|<x\},\quad F_{n+1}(x)=\mathbf P\{|\xi_n-\eta_n|<x\}, $$
and prove two theorems concerning the limiting behaviour of $F_n(x)$.

Full text: PDF file (687 kB)

English version:
Theory of Probability and its Applications, 1969, 14:4, 668–681

Bibliographic databases:

Received: 01.07.1968

Citation: S. S. Vallander, I. A. Ibragimov, N. G. Lindtrop, “On limiting distributions for moduli of sequential differences of independent variables”, Teor. Veroyatnost. i Primenen., 14:4 (1969), 693–707; Theory Probab. Appl., 14:4 (1969), 668–681

Citation in format AMSBIB
\Bibitem{ValIbrLin69}
\by S.~S.~Vallander, I.~A.~Ibragimov, N.~G.~Lindtrop
\paper On limiting distributions for moduli of sequential differences of independent variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1969
\vol 14
\issue 4
\pages 693--707
\mathnet{http://mi.mathnet.ru/tvp1481}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=264743}
\zmath{https://zbmath.org/?q=an:0204.51204|0185.46501}
\transl
\jour Theory Probab. Appl.
\yr 1969
\vol 14
\issue 4
\pages 668--681
\crossref{https://doi.org/10.1137/1114082}


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