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arXiv · 0711.1068

A conservative evolution of the Brownian excursion

Lorenzo Zambotti
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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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Lorenzo Zambotti. 2007-11-07. A conservative evolution of the Brownian excursion. https://arxiv.org/abs/0711.1068

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