A conservative evolution of the Brownian excursion
Lorenzo Zambotti, University of Paris 6, France
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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