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5 papers
Introducing smooth amnesia to the memory of the Elephant Random Walk
Lucile Laulin
This paper is devoted to the asymptotic analysis of the amnesic elephant random walk (AERW) using a martingale approach. More precisely, our analysis relies on asymptotic results f…
New insights on the reinforced Elephant Random Walk using a martingale approach
Lucile Laulin
This paper is devoted to the asymptotic analysis of the reinforced elephant random walk (RERW) using a martingale approach. In the diffusive and critical regimes, we establish the…
A martingale approach for Pólya urn processes
Lucile Laulin
This paper is devoted to a direct martingale approach for P{ó}lya urn models asymptotic behaviour. A P{ó}lya process is said to be small when the ratio of its remplacement matrix e…
On the center of mass of the elephant random walk
Bernard Bercu, Lucile Laulin
Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its…
On the multi-dimensional elephant random walk
Bernard Bercu, Lucile Laulin
The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional elephant random walk (MERW). It is a non-Markovian random walk which has a complete mem…