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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 1,
pages 39 - 61
 

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 (W (.)) is proved. This representation is then used to prove a large deviations principle for the family (Ge(W (.)))   ,
         e>0 where Ge  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.

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