Sample path large deviations for super-Brownian motion

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 Hoelder norm of index #alpha#<1/2 of the process t#-># left angle f, X_t right angle possesses some finite exponential moments provided the function f is smooth. (orig.)SIGLEAvailable from TIB Hannover: RR 6329(96-1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbibliothekrev. ed.DEGerman