Summary
We derive two large deviation principles of Freidlin-Wentzell type for rescaled super-Brownian motion. For one of the appearing rate functions an integral representation is given and interpreted as ‘Kakutani-Hellinger energy’. As a tool we develop estimates for the Laplace functionals of (historical) super-Brownian motion and certain maximal inequalities. Also it is shown that the Hölder norm of index α<1/2 of the processt↦〈f, X t 〉 possesses some finite exponential moments provided the functionf is smooth.
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This work was supported in part by the Graduiertenkolleg “Algebraische, analytische und geometrische Methoden und ihre Wechselwirkung in der modernen Mathematik”, Bonn