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A variational representation for positive functionals of infinite dimensional Brownian motion

Budhira A., Dupuis P.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 1

39--61

A variational representation for positive functionals of a Hilbert space valued Wiener process (W(-)) is proved. This representation is then used to prove a large deviations principle for the family {Gε(W{‧))} ε>0 where G is an appropriate family of measurable maps from the Wiener space to some Polish space.