A Note on Transience of Generalized Multi-Dimensional Excited Random Walks

Rodrigo B. Alves (), Giulio Iacobelli () and Glauco Valle ()
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Rodrigo B. Alves: FGV
Giulio Iacobelli: Universidade Federal do Rio de Janeiro
Glauco Valle: Universidade Federal do Rio de Janeiro

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1927-1943

Abstract: Abstract We consider a variant of the generalized excited random walk (GERW) in dimension $$d\ge 2$$ d ≥ 2 where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays more slowly than $$n^{-\beta _0}$$ n - β 0 (n is time), where $$\beta _0$$ β 0 depends on the transitions of the process, the GERW is transient in the direction of the drift.

Keywords: Excited random walks; Non-Markovian processes; Transience; 60K37 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01311-3

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