4 papers
A central limit theorem for unbalanced step-reinforced random walks
Zhishui Hu, Liang Dong
In this paper, we study a class of unbalanced step-reinforced random walks that unifies the elephant random walk, the positively step-reinforced random walk, and the negatively ste…
Profinite Direct Sums with Applications to Profinite Groups of Type
Jiacheng Tang
We show that the "profinite direct sum" is a good notion of infinite direct sums for profinite modules having properties similar to direct sums of abstract modules. For example, th…
Strong Approximations in the Almost Sure Central Limit Theorem and Limit Behavior of the Center of Mass
Zhishui Hua, Wei Wanga, Liang Dong
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterat…
Strong limit theorems for step-reinforced random walks
Zhishui Hu, Yiting Zhang
A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk…