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

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
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### References:

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