3 papers
math.PR2023
Rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales
Xiequan Fan, Zhonggen Su
We give some rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales with differences having finite variances. For the Kolmogorov distances…
math.PR2023
Rates of convergence in the central limit theorem for the elephant random walk with random step sizes
Jérôme Dedecker, Xiequan Fan, Haijuan Hu +1
In this paper, we consider a generalization of the elephant random walk model. Compared to the usual elephant random walk, an interesting feature of this model is that the step siz…
math.PR2016
On McDiarmid's inequality for Hamming distance
Xiequan Fan
We improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variable…