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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 37 open journal systems 


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.


Full text: PDF

Pages: 1096-1119

Published on: July 9, 2008


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Electronic Journal of Probability. ISSN: 1083-6489