Limit theorems for a random walk with memory perturbed by a dynamical system

Author(s)

Coletti, Cristian F. ^[1] ; de Lima, Lucas R. ^[1] ; Gava, Renato J. ^[2] ; Luiz, Denis A. ^[1]

Affiliation

^[1] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Ave Estados 5001, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Estat, Rod Washington Luiz, Km 235, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 61, n. 10 OCT 1 2020.
• Web of Science Citations: 0

Abstract

We introduce a new random walk with unbounded memory obtained as a mixture of the elephant random walk and the dynamic random walk, which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture, the distribution of the increments of the resulting random process is time dependent. We prove a strong law of large numbers for the DERW and, in a particular case, we provide an explicit expression for its speed. Finally, we give sufficient conditions for the central limit theorem and the law of the iterated logarithm to hold. (AU)

• FAPESP's process: 19/19056-2 - Asymptotic shape for subadditive processes on groups and on random geometric graphs
• Grantee: Lucas Roberto de Lima
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/04764-9 - Random walks with unbounded memory
• Grantee: Renato Jacob Gava
• Support Opportunities: Scholarships abroad - Research