Continuous time vertex-reinforced jump processes

B Davis, S Volkov

Research output: Contribution to journalArticle (Academic Journal)peer-review

22 Citations (Scopus)

Abstract

We study the continuous time integer valued process X-t, t greater than or equal to 0, 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 lim(t-->infinity) max(0less than or equal tosless than or equal tot) X-s/log t = 2.768...
Translated title of the contributionContinuous time vertex-reinforced jump processes
Original languageEnglish
Pages (from-to)281 - 300
Number of pages20
JournalProbability Theory and Related Fields
Volume123 (2)
Publication statusPublished - Jun 2002

Bibliographical note

Publisher: Springer-Verlag

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