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Analysis of Algorithms by the Contraction Method: Additive and Max-recursive Sequences

In: Interacting Stochastic Systems

Author

Listed:
  • Ralph Neininger

    (J. W. Goethe University, Department of Mathematics)

  • Ludger Rüschendorf

    (University of Freiburg, Department of Mathematics)

Abstract

Summary In the first part of this paper we give an introduction to the contraction method for the analysis of additive recursive sequences of divide and conquer type. Recently some general limit theorems have been obtained by this method based on a general transfer theorem. This allows to conclude from the recursive structure and the asymptotics of first moment(s) the limiting distribution. In the second part we extend the contraction method to max-recursive sequences. We obtain a general existence and uniqueness result for solutions of stochastic equations including maxima and sum terms. We finally derive a general limit theorem for max-recursive sequences of the divide and conquer type.

Suggested Citation

  • Ralph Neininger & Ludger Rüschendorf, 2005. "Analysis of Algorithms by the Contraction Method: Additive and Max-recursive Sequences," Springer Books, in: Jean-Dominique Deuschel & Andreas Greven (ed.), Interacting Stochastic Systems, pages 435-450, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27110-9_20
    DOI: 10.1007/3-540-27110-4_20
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