Abstract
Recently, the elephant random walk has attracted much attention. A wide range of literature studies are available for the asymptotic behavior of the process, such as central limit theorems, functional limit theorems, and the law of the iterated logarithm. However, there is no result concerning the Wasserstein-1 distance for normal approximations. In this paper, we show that the Wasserstein-1 distance in the central limit theorem is totally different when a memory parameter p belongs to one of the three cases 0 < p < 1/2, 1/2 < p < 3/4, and p = 3/4.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.