A VARIATIONAL REPRESENTATION FOR POSITIVE FUNCTIONALS OF
INFINITE DIMENSIONAL BROWNIAN MOTION
Amarjit Budhiraja
Paul Dupuis
Abstract: A variational representation for positive functionals of a Hilbert space valued
Wiener process is proved. This representation is then used to prove a large
deviations principle for the family where is an appropriate family of
measurable maps from the Wiener space to some Polish space.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: Large deviations, Laplace principle, stochastic control,
cylindrical Brownian motion, stochastic evolution equations, infinite dimensional stochastic
calculus.