In stochastic calculus, the Boué–Dupuis formula is variational representation for Wiener functionals. The representation has application in finding large deviation asymptotics.
The theorem was proven in 1998 by Michelle Boué and Paul Dupuis. In 2000 the result was generalized to infinite-dimensional Brownian motions and in 2009 extended to abstract Wiener spaces.
Boué–Dupuis formula.
Let formula_1 be the classical Wiener space and formula_2 be a formula_3-dimensional standard Brownian motion. Then for all bounded and measurable functions
formula_4 we have the following variational representation
formula_5
where: