A large deviation principle for the Brownian snake

Laurent Serlet

Stochastic Processes and their Applications, 1997, vol. 67, issue 1, 101-115

Abstract: We consider the path-valued process called the Brownian snake, conditioned so that its lifetime process is a normalised Brownian excursion. This process denoted by ((Ws, [xi]s); s [set membership, variant] [0, 1]) is closely related to the integrated super-Brownian excursion studied recently by several authors. We prove a large deviation principle for the law of (([var epsilon]Ws([zeta]s), [var epsilon]2/3[zeta]s); s [epsilon] [0, 1]) as [var epsilon][downwards arrow]0. In particular, we give an explicit formula for the rate function of this large deviation principle. As an application we recover a result of Dembo and Zeitouni.

Keywords: Brownian; snake; Large; deviation; principle; Super-Brownian; motion; Rate; function (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (4)

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