Open Access
2002 Hitting Properties of a Random String
Carl Mueller, Roger Tribe
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Electron. J. Probab. 7: 1-29 (2002). DOI: 10.1214/EJP.v7-109


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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Carl Mueller. Roger Tribe. "Hitting Properties of a Random String." Electron. J. Probab. 7 1 - 29, 2002.


Accepted: 12 April 2002; Published: 2002
First available in Project Euclid: 16 May 2016

zbMATH: 1010.60059
MathSciNet: MR1902843
Digital Object Identifier: 10.1214/EJP.v7-109

Primary: 60H15
Secondary: 35L05 , 35R60

Keywords: martingale , random set , strong martingale property

Vol.7 • 2002
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