11 citations · 11 across the 1 of their papers we have counts for
4 papers
A universal scaling limit for diffusive amnesic step-reinforced random walks
Marco Bertenghi, Lucile Laulin
We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suita…
Joint invariance principles for random walks with positively and negatively reinforced steps
Marco Bertenghi, Alejandro Rosales-Ortiz
Given a random walk with typical step distributed according to some fixed law and a fixed parameter , the associated positively step-reinforced random walk is…
Asymptotic Normality of Superdiffusive Step-Reinforced Random Walks
Marco Bertenghi
In this article we establish for the superdiffusive regime that the fluctuations of a general step-reinforced random walk around , where $(a_n)_{n \in…
Functional limit theorems for the Multi-dimensional Elephant Random Walk
Marco Bertenghi
In this article we shall derive functional limit theorems for the multi-dimensional elephant random walk (MERW) and thus extend the results provided for the one-dimensional margina…