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Pré-Publication, Document De Travail Année : 2015

Persistent random walks

Résumé

We consider a walker that at each step keeps the same direction with a probability that depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent random walk and give the conditions of recurrence or transience in terms of ”transition” probabilities to keep on the same direction or to change, without assuming that the latter admits any stationary probability. Examples are exhibited when this process is recurrent even if the random walk is not symmetric.
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Dates et versions

hal-01135794 , version 1 (25-03-2015)
hal-01135794 , version 2 (13-09-2015)

Identifiants

  • HAL Id : hal-01135794 , version 1

Citer

Peggy Cénac, Basile de Loynes, Arnaud Le Ny, Yoann Offret. Persistent random walks. 2015. ⟨hal-01135794v1⟩
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