2022/02/27 by János Engländer, Englander, Janos, С. С. Волков +1
Mathematics · Computer Science · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.2202.13399
Recently, in ["The coin-turning walk and its scaling limit", Electronic Journal of Probability, 25 (2020)], the ``coin-turning walk'' was introduced on \mathbb Z. It is a non-Markovian process where the steps form a (possibly) time-inhomogeneous Markov chain. In this article, we follow up the investigation by introducing analogous processes in \mathbb Zd, d≥ 2: at time n the direction of the process is ``updated'' with probability pn; otherwise the next step repeats the previous one. We study some of the fundamental properties of these walks, such as transience/recurrence and scaling limits. Our results complement previous ones in the literature about ``correlated'' (or ``Newtonian'') and ``persistent'' random walks.