In stochastic calculus, the BouĂ©âDupuis 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. [1] In 2000 [2] the result was generalized to infinite-dimensional Brownian motions and in 2009 [3] extended to abstract Wiener spaces.
Let be the classical Wiener space and be a -dimensional standard Brownian motion. Then for all bounded and measurable functions we have the following variational representation
where:
In stochastic calculus, the BouĂ©âDupuis 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. [1] In 2000 [2] the result was generalized to infinite-dimensional Brownian motions and in 2009 [3] extended to abstract Wiener spaces.
Let be the classical Wiener space and be a -dimensional standard Brownian motion. Then for all bounded and measurable functions we have the following variational representation
where: