Deviation inequalities for the elephant random walk with random step sizes

Recently, the asymptotic behaviors of the elephant random walk have attracted a lot of attentions. Many interesting properties for the elephant random walk have been established in the past few years, such as strong invariance principles, central limit theorems, functional limit theorems and law of large numbers. In this paper, we give some deviation inequalities for the elephant random walk with random step sizes with various moment conditions. More precisely, we are interested in giving quantitative estimates for the convergence rates in the law of large numbers.