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Continuous time vertex-reinforced jump processes

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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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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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Keywords

  • Continuous Time
  • Jump Process