Sample path large deviations for super-Brownian motion (Q1912569)

The author gives 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 the author develops estimates for the Laplace functionals of (historical) super-Brownian motion and certain maximal inequalities. Also it is shown that the Hölder norm of index \(\alpha < 1/2\) of the process \(t \mapsto \langle f,X_t \rangle\) possesses some finite exponential moments provided the function \(f\) is smooth. It is interesting that the rate functions can be expressed by Kakutani-Hellinger distance.