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2008 A conservative evolution of the Brownian excursion
Lorenzo Zambotti
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Electron. J. Probab. 13: 1096-1119 (2008). DOI: 10.1214/EJP.v13-525


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. "A conservative evolution of the Brownian excursion." Electron. J. Probab. 13 1096 - 1119, 2008.


Accepted: 9 July 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1187.60063
MathSciNet: MR2424988
Digital Object Identifier: 10.1214/EJP.v13-525

Primary: 60J65
Secondary: 37L40 , 60G15 , 60H07 , 60H15

Keywords: Brownian excursion , Brownian meander , singular conditioning , Stochastic partial differential equations with reflection

Vol.13 • 2008
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