A conservative evolution of the Brownian excursion
Abstract
We consider the problem of conditioning the Brownian excursion to have a fixed time average over the interval [0,1] and we study an associated stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution.
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Pages: 1096-1119
Publication Date: July 9, 2008
DOI: 10.1214/EJP.v13-525
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