Complementary asymptotic analysis for a minimal random walk

2024/04/25 by Coletti, Cristian F., González-Navarrete, Manuel, Guevara, Víctor Hugo Vázquez · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2404.16800

Abstract

We discuss a complementary asymptotic analysis of the so called minimal random walk. More precisely, we present a version of the almost sure central limit theorem as well as a generalization of the recently proposed quadratic strong laws. In addition, alternative demonstrations of the functional limit theorems will be supplied based on a Pólya urn scheme instead of a martingale approach.

Cited by

• Functional central limit theorem for dependent models with finite memory

Related

• On the asymptotics of a lazy reinforced random walk
• Strong Approximations in the Almost Sure Central Limit Theorem and Limit Behavior of the Center of Mass
• Quantitative recurrence results for random walks
• Polya's random walk theorem
• The quenched central limit theorem for a model of random walk in random\n environment