Cramér moderate deviations for the elephant random walk
Xiequan Fan, Haijuan Hu, Xiaohui Ma
Abstract
Abstract We establish some limit theorems for the elephant random walk (ERW), including Berry–Esseen’s bounds, Cramér moderate deviations and local limit theorems. These limit theorems can be regarded as refinements of the central limit theorem for the ERW. Moreover, by these limit theorems, we conclude that the convergence rate of normal approximations and the domain of attraction of normal distribution mainly depend on a memory parameter p which lies between 0 and 3/4.
Topics & Concepts
Limit (mathematics)Random walkMathematicsCentral limit theoremUniform limit theoremConvergence (economics)Normal distributionDomain (mathematical analysis)Large deviations theoryStatistical physicsMathematical analysisCombinatoricsStatisticsPhysicsEconomic growthEconomicsStochastic processes and statistical mechanicsBayesian Methods and Mixture ModelsDiffusion and Search Dynamics