Hitting Properties of a Random String

Carl Mueller (University of Rochester)
Roger Tribe (University of Warwick)


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.

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Pages: 1-29

Publication Date: April 12, 2002

DOI: 10.1214/EJP.v7-109

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