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.
Citation
Carl Mueller. Roger Tribe. "Hitting Properties of a Random String." Electron. J. Probab. 7 1 - 29, 2002. https://doi.org/10.1214/EJP.v7-109
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