Open Access
1997 Finite Width For a Random Stationary Interface
Carl Mueller, Roger Tribe
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Electron. J. Probab. 2: 1-27 (1997). DOI: 10.1214/EJP.v2-21


We study the asymptotic shape of the solution $u(t,x) \in [0,1]$ to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is $u(0,x)$ is 0 for all large positive $x$ and $u(0,x)$ is 1 for all large negitive $x$. The special form of the noise term preserves this property at all times $t \geq 0$. The main result is that, in contrast to the deterministic heat equation, the width of the interface remains stochastically bounded.


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Carl Mueller. Roger Tribe. "Finite Width For a Random Stationary Interface." Electron. J. Probab. 2 1 - 27, 1997.


Accepted: 16 October 1997; Published: 1997
First available in Project Euclid: 26 January 2016

zbMATH: 0890.60056
MathSciNet: MR1485116
Digital Object Identifier: 10.1214/EJP.v2-21

Primary: 60H15
Secondary: 35R60

Keywords: Duality , Stochastic partial differential equations , Travelling waves , White noise

Vol.2 • 1997
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