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Saddlepoint expansions for sums of Markov dependent variables on a continuous state space
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  • Published: June 1991

Saddlepoint expansions for sums of Markov dependent variables on a continuous state space

  • Jens Ledet Jensen1 

Probability Theory and Related Fields volume 89, pages 181–199 (1991)Cite this article

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Summary

Based on the conjugate kernel studied in Iscoe et al. (1985) we derive saddlepoint expansions for either the density or distribution function of a sumf(X 1)+...+f(X n ), where theX i 's constitute a Markov chain. The chain is assumed to satisfy a strong recurrence condition which makes the results here very similar to the classical results for i.i.d. variables. In particular we establish also conditions under which the expansions hold uniformly over the range of the saddlepoint. Expansions are also derived for sums of the formf(X 1,X 0)+f(X 2,X 1)+...+f(X n ,X n−1) although the uniformity result just mentioned does not generalize.

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Authors and Affiliations

  1. Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, DK-8000, Aarhus C, Denmark

    Jens Ledet Jensen

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  1. Jens Ledet Jensen
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Jensen, J.L. Saddlepoint expansions for sums of Markov dependent variables on a continuous state space. Probab. Th. Rel. Fields 89, 181–199 (1991). https://doi.org/10.1007/BF01366905

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  • Received: 19 October 1990

  • Issue Date: June 1991

  • DOI: https://doi.org/10.1007/BF01366905

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Keywords

  • Distribution Function
  • Markov Chain
  • State Space
  • Stochastic Process
  • Probability Theory
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