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On the Rate of Convergence of the Ross Approximation to the Renewal Function
Published online by Cambridge University Press: 27 July 2009
Abstract
Consider a renewal process [N(t), t>0]. For fixed t > 0 and each n ≥ 1, let yn,1, …, Yn,n be independent exponentials each having mean t/n, independent of the renewal process. Ross [2] developed a recursion for the sequence of approximations mn = EN(Yn,1 + … + Yn,n) that converges to m(t)if the renewal function m(·) = EN(·) is continuous at t > 0. In this note, we derive an upper bound on the rate of convergence of this sequence under mild conditions on m near t. Tightness of this bound is discussed in terms of regularity conditions on m.
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- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 207 - 211
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- Copyright © Cambridge University Press 1996
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