Universality of Noise Reinforced Brownian Motions
| Autor: | Jean Bertoin |
|---|---|
| Přispěvatelé: | Bertoin, Jean, University of Zurich, Vares, M E, Fernandez, R, Fontes, L R, Newman, Charles M |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
340 Law 610 Medicine & health 60G50 (Primary) 60G51 60K35 (Secondary) Noise (electronics) Combinatorics symbols.namesake 510 Mathematics Invariance Principle Elephant Random Walk Mathematics Subject Classification: 60G50 FOS: Mathematics Gaussian process Brownian motion Physics Invariance principle Probability (math.PR) Universality (philosophy) Covariance Random walk Reinforcement 10123 Institute of Mathematics Scaling limit 60K35 symbols Mathematics - Probability 60G51 |
| Zdroj: | Progress in Probability ISBN: 9783030607531 |
| Popis: | A noise reinforced Brownian motion is a centered Gaussian process $\hat B=(\hat B(t))_{t\geq 0}$ with covariance $E(\hat B(t)\hat B(s))=(1-2p)^{-1}t^ps^{1-p} \quad \text{for} \quad 0\leq s \leq t,$ where $p\in(0,1/2)$ is a reinforcement parameter. Our main purpose is to establish a version of Donsker's invariance principle for a large family of step-reinforced random walks in the diffusive regime, and more specifically, to show that $\hat B$ arises as the universal scaling limit of the former. This extends known results on the asymptotic behavior of the so-called elephant random walk. Comment: An unnecessary assumption for the validity of the invariance principle which was made in the first draft has been removed (15 pages) |
| Databáze: | OpenAIRE |
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