1 results
Second-order approximations for certain stopped sums in extended renewal theory
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- Journal:
- Advances in Applied Probability / Volume 20 / Issue 2 / June 1988
- Published online by Cambridge University Press:
- 01 July 2016, pp. 391-410
- Print publication:
- June 1988
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- Article
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Let (X0, Y0), (X1, Y1), · ·· be a sequence of independent two-dimensional random vectors such that (X1, Y1), (X2, 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, Y0) and (X1, Y1) 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, Χ1 are both almost surely non-negative and
