A conservative evolution of the Brownian excursion
Probability
2007-11-08 v1
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.
Keywords
Cite
@article{arxiv.0711.1068,
title = {A conservative evolution of the Brownian excursion},
author = {Lorenzo Zambotti},
journal= {arXiv preprint arXiv:0711.1068},
year = {2007}
}