### Recurrence and transience preservation for vertex reinforced jump processes in one dimension

Burgess Davis and Noah Dean
Source: Illinois J. Math. Volume 54, Number 3 (2010), 869-893.

#### Abstract

We show that the application of linear vertex reinforcement to one dimensional nearest neighbor Markov processes, yielding associated vertex reinforced jump processes, preserves both recurrence and transience. The analog for discrete time linear bond reinforcement is due to Takeshima. This together with another result we prove adds to the numerous known parallels between these two reinforcements. Martingales are the primary tool used to study vertex reinforced jump processes.

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Primary Subjects: 60K37, 60J10
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Permanent link to this document: http://projecteuclid.org/euclid.ijm/1336049980
Mathematical Reviews number (MathSciNet): MR2928340
Zentralblatt MATH identifier: 06122080

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