Introducing smooth amnesia to the memory of the Elephant Random Walk
Language
en
Article de revue
This item was published in
Electronic Communications in Probability. 2022-10-28, vol. 27
Institute of Mathematical Statistics (IMS)
English Abstract
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 for multidimensional martingales with matrix ...Read more >
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 for multidimensional martingales with matrix normalization. In the diffusive and critical regimes, we establish the almost sure convergence and the quadratic strong law for the position of the AERW. The law of iterated logarithm is given in the critical regime. The distributional convergences of the AERW to Gaussian processes are also provided. In the superdiffusive regime, we prove the distributional convergence as well as the mean square convergence of the AERW.Read less <
English Keywords
Elephant random walk
Almost sure convergence
Multi-dimensional martingales
Amnesic random walk
Asymptotic normality
Distributional convergence
Origin
Hal imported