@article{EJP109,
author = {Carl Mueller and Roger Tribe},
title = {Hitting Properties of a Random String},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {7},
year = {2002},
keywords = {Martingale, random set, strong martingale property},
abstract = {We consider Funaki's model of a random string taking values in $\mathbf{R}^d$. It is specified by the following stochastic PDE, \[ \frac{\partial u(x)}{\partial t}=\frac{\partial^2 u(x)}{\partial x^2} +\dot{W}. \] where $\dot{W}=\dot{W}(x,t)$ is two-parameter white noise, also taking values in $\mathbf{R}^d$. We find the dimensions in which the string hits points, and in which it has double points of various types. We also study the question of recurrence and transience.},
pages = {no. 10, 1-29},
issn = {1083-6489},
doi = {10.1214/EJP.v7-109},
url = {http://ejp.ejpecp.org/article/view/109}}