@article{ECP2763,
author = {Kenneth Alexander},
title = {Controlled random walk with a target site},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {18},
year = {2013},
keywords = {random walk, stochastic control},
abstract = {We consider a symmetric simple random walk $\{W_i\}$ on $\mathbb{Z}^d, d=1,2$, in which the walker may choose to stand still for a limited time. The time horizon is $n$, the maximum consecutive time steps which can be spent standing still is $m_n$ and the goal is to maximize $\mathbb{P}(W_n=0)$. We show that for $d=1$, if $m_n \gg (\log n)^{2+\gamma}$ for some $\gamma>0$, there is a strategy for each $n$ yielding $\mathbb{P}(W_n = 0) \to 1$. For $d=2$, if $m_n \gg n^\epsilon$ for some $\epsilon>0$ then there are strategies yielding $\liminf_n \mathbb{P}(W_n=0)>0$.},
pages = {no. 43, 1-6},
issn = {1083-589X},
doi = {10.1214/ECP.v18-2763},
url = {http://ecp.ejpecp.org/article/view/2763}}