## 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 contribution | Continuous time vertex-reinforced jump processes |
---|---|

Original language | English |

Pages (from-to) | 281 - 300 |

Number of pages | 20 |

Journal | Probability Theory and Related Fields |

Volume | 123 (2) |

Publication status | Published - Jun 2002 |