Abstract
The elephant random walk (ERW) is a discrete-time random walk on Z with a memory about the whole past. It has been shown that the asymptotic behavior of the ERW depends heavily on a memory parameter 0≤p≤1. In this work, we establish the strong invariance principle for the ERW in the diffusive regime 0≤p<3/4 and the critical regime p = 3/4, which enhances the known results of Coletti, Gava and Schütz.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
