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Explosions in Markov Processes and Submartingale Convergence.

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Athens Conference on Applied Probability and Time Series Analysis

Part of the book series: Lecture Notes in Statistics ((LNS,volume 114))

Abstract

Conditions for nonexplosions and explosions in Markov pure jump processes are given in terms of the rate of change in the process. We show how these conditions follow from a submartingale convergence theorem. As a corollary, new conditions for nonexplosions in Birth-Death processes in terms of the survival rate are obtained.

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Research supported by the Australian Research Council

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References

  1. Breiman L.(1968). Probability. Addison-Wesley, Reading, Ma.

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  2. Chung, K.L. (1967). Markov Chains with Stationary Transition Probabilities. Springer, New York.

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Author information

Authors and Affiliations

  1. University of Frankfurt, Germany

    G. Kersting

  2. University of Melbourne, Australia

    F. C. Klebaner

Authors
  1. G. Kersting
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  2. F. C. Klebaner
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Editor information

Editors and Affiliations

  1. Stochastic Analysis Program, SMS, Australian National University, Canberra, ACT, 0200, Australia

    C. C. Heyde

  2. Academy of Sciences, Mathematical Institute, Vavilov Street 42, Moscow, 333, Russia

    Yu V. Prohorov

  3. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Ronald Pyke

  4. Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA

    S. T. Rachev

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© 1996 Springer Science+Business Media New York

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Kersting, G., Klebaner, F.C. (1996). Explosions in Markov Processes and Submartingale Convergence.. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0749-8_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94788-4

  • Online ISBN: 978-1-4612-0749-8

  • eBook Packages: Springer Book Archive

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