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Finite-time implications of relaxation times for stochastically monotone processes
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  • Published: March 1988

Finite-time implications of relaxation times for stochastically monotone processes

  • David J. Aldous1 nAff2 

Probability Theory and Related Fields volume 77, pages 137–145 (1988)Cite this article

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  • 6 Citations

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Summary

For a continuous-time finite state Markov process with stationary distribution π, it is well-known thatP i(X t=j)-πj isO(e -λt ) ast→∞, for a certain λ. For a stochastically monotone process for which the reversed process is also stochastically monotone, one can obtain bounds valid for allt. Precisely,\(\sum\limits_i {\pi _j \mathop {\max |}\limits_j P_i } (X_t \leqq j) - \pi [0,j]| \leqq 2(\lambda t + 2)\) exp(-λt). The proof exploits duality for stochastically monotone processes.

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Author information

Author notes
  1. David J. Aldous

    Present address: INSA Toulouse, Tou7louse, France

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA, USA

    David J. Aldous

Authors
  1. David J. Aldous
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Additional information

Research supported by National Science Foundation Grant MCS 84-03239

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Cite this article

Aldous, D.J. Finite-time implications of relaxation times for stochastically monotone processes. Probab. Th. Rel. Fields 77, 137–145 (1988). https://doi.org/10.1007/BF01848136

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  • Received: 07 August 1986

  • Revised: 17 September 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF01848136

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Keywords

  • Relaxation Time
  • Stochastic Process
  • Probability Theory
  • Markov Process
  • Stationary Distribution
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