A large deviation principle for the Brownian snake. (English) Zbl 0889.60026

Serlet, L.

Stochastic Processes Appl. 67, No. 1, 101-115 (1997).

Summary: 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 \(((W_{s}, \zeta _s); s\in [0,1])\) is closely related to the integrated super-Brownian excursion studied recently by several authors. We prove a large deviation principle for the law of \(((\varepsilon W_s (\zeta _s), \varepsilon ^{2/3} \zeta _s)\); \(s\in [0,1])\) as \(\varepsilon \downarrow 0\). 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.

MSC:

60F10	Large deviations
60G15	Gaussian processes
60J25	Continuous-time Markov processes on general state spaces

Keywords:

Brownian snake; large deviation principle; super-Brownian motion; rate function

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