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A large deviation principle for the Brownian snake

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  • Serlet, Laurent

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.

Suggested Citation

  • Serlet, Laurent, 1997. "A large deviation principle for the Brownian snake," Stochastic Processes and their Applications, Elsevier, vol. 67(1), pages 101-115, April.
    • Handle: RePEc:eee:spapps:v:67:y:1997:i:1:p:101-115
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    Citations

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    Cited by:

    1. Schied, Alexander, 1997. "Moderate deviations and functional LIL for super-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 11-25, December.
    2. Fatheddin, Parisa & Xiong, Jie, 2015. "Large deviation principle for some measure-valued processes," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 970-993.
    3. Serlet, Laurent, 2009. "New large deviation results for some super-Brownian processes," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1696-1724, May.
    4. Jean-François Marckert & Abdelkader Mokkadem, 2003. "States Spaces of the Snake and Its Tour—Convergence of the Discrete Snake," Journal of Theoretical Probability, Springer, vol. 16(4), pages 1015-1046, October.

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