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Second-order approximations for certain stopped sums in extended renewal theory

Published online by Cambridge University Press:  01 July 2016

Gerold Alsmeyer
Gerold Alsmeyer*
Affiliation:
University of Kiel
*
∗Postal address: Mathematisches Seminar, Universität Kiel, Olshausenstraβe 40, D-2300 Kiel 1, W. Germany.
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Abstract

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

Keywords

I.I.D. TWO-DIMENSIONAL RANDOM VECTORSRENEWAL REWARD PROCESSESFIRST-PASSAGE TIMESRANDOMLY INDEXED PARTIAL SUMS
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 391 - 410
Copyright
Copyright © Applied Probability Trust 1988 

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