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Continuous time vertex-reinforced jump processes
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  • Published: June 2002

Continuous time vertex-reinforced jump processes

  • Burgess Davis1 &
  • Stanislav Volkov2 

Probability Theory and Related Fields volume 123, pages 281–300 (2002)Cite this article

  • 139 Accesses

  • 29 Citations

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Abstract.

 We study the continuous time integer valued process , which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent at that neighbor. We show that the proportion of the time before t which this process spends at integers j converges to positive random variables V j , which sum to one, and whose joint distribution is explicitly described. We also show

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Authors and Affiliations

  1. Department of Statistics, Purdue University, West Lafayette, IN 47907, USA. e-mail: bdavis@stat.purdue.edu, , , , , , US

    Burgess Davis

  2. Department of Mathematics, University of Bristol, Bristol, BS81TW, UK. e-mail: S.Volkov@bristol.ac.uk, , , , , , GB

    Stanislav Volkov

Authors
  1. Burgess Davis
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  2. Stanislav Volkov
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Received: 19 December 2000 / Revised version: 1 November 2001 / Published online: 17 May 2002

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Davis, B., Volkov, S. Continuous time vertex-reinforced jump processes. Probab. Theory Relat. Fields 123, 281–300 (2002). https://doi.org/10.1007/s004400100189

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  • Issue Date: June 2002

  • DOI: https://doi.org/10.1007/s004400100189

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Keywords

  • Continuous Time
  • Jump Process
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