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Discrete Time Renewal Processes

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Renewal Processes

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

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Abstract

In this chapter, we give a review of discrete renewal theory and prove the basic theorems for renewal sequences. We provide two different proofs of the theorem of Erdös-Feller-Pollard. Using extensions of a theorem of Wiener, we also obtain several rate of convergence results in discrete renewal theory.

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References

  1. Barbu, V.S., Limnios, N.: Semi-Markov Chains and Hidden Semi-Markov Models Toward Applications. Springer, New York (2008)

    Google Scholar 

  2. Borovkov, A.A.: Stochastic Processes in Queueing Theory. Springer, New York (1976)

    Book  MATH  Google Scholar 

  3. Erdös, P., Feller, W., Pollard, H.: A property of power series with positive coefficients. Bull. Am. Math. Soc. 55(2), 201–204 (1949)

    Article  MATH  Google Scholar 

  4. Feller, W.: An Introduction to Probability Theory and its Applications, vol. I. Wiley, New York (1968)

    MATH  Google Scholar 

  5. Rogozin, B.A.: Asymptotics of the coefficients in the Lévy-Wiener theorems on absolutely convergent trigonometric series. Sib. Math. J. 14, 1304–1312 (1973)

    MATH  MathSciNet  Google Scholar 

  6. Rogozin, B.A.: An estimate of the remainder term in limit theorems of renewal theory. Theory Prob. Appl. 18, 662–677 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  7. Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1970)

    Google Scholar 

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Correspondence to Kosto V. Mitov .

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Mitov, K.V., Omey, E. (2014). Discrete Time Renewal Processes. In: Renewal Processes. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-05855-9_2

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