Abstract
Let (X0, Y0 ), (X1, Y 1), · ·· be a sequence of independent two-dimensional random vectors such that (X 1, Y 1), (X 2 , Y2 ), · ·· are i.i.d. Let {(Sn , Un )} n≧0 be the associated sum process, and define for t ≧ 0 Under suitable conditions on (X0 , Y 0) and (X1, Y 1) we derive expansions up to vanishing terms, as t→∞, for EUT(t) , Var UT(t) and Cov (UT(t) , T(t)). Corresponding results will be obtained for EUN(t) , Var UN (t) and Cov (UN (t) , N(t)) when X0, Χ 1 are both almost surely non-negative and
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