A strong invariance principle for the elephant random walk
| Autor: | Renato J. Gava, Cristian F. Coletti, Gunter M. Schütz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Invariance principle Probability (math.PR) Statistical and Nonlinear Physics Law of the iterated logarithm Critical value Random walk 01 natural sciences 010305 fluids & plasmas Mathematics::Probability 0103 physical sciences FOS: Mathematics Almost surely Statistics Probability and Uncertainty 010306 general physics Scaling Brownian motion Mathematics - Probability Mathematical physics Mathematics Central limit theorem |
| Popis: | We consider a non-Markovian discrete-time random walk on $\mathbb{Z}$ with unbounded memory called the elephant random walk (ERW). We prove a strong invariance principle for the ERW. More specifically, we prove that, under a suitable scaling and in the diffusive regime as well as at the critical value $p_c=3/4$ where the model is marginally superdiffusive, the ERW is almost surely well approximated by a Brownian motion. As a by-product of our result we get the law of iterated logarithm and the central limit theorem for the ERW. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|