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Contents of PMS, Vol. 4, Fasc. 2,
pages 207 - 219
 

ASYMPTOTIC EXPANSIONS FOR CONDITIONAL DISTRIBUTIONS: THE LATTICE CASE

Christian Hipp

Abstract: It is shown that the conditional distribution of X + ...+ X , 1 n given Y + ...+Y = y, 1 n admits an asymptotic expansion whenever (X ,Y ), (X ,Y ),... 1 1 2 2 is a sequence of independent identically distributed lattice random vectors and y lies in a set A(n) for which P(Y + ...+ Y (- A(n)) 1 n can be neglected. Explicit formulas are given for the terms of order  n -1/2 and n-1.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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