The Boué–Dupuis formula and the exponential hypercontractivity in the Gaussian space
The Boué–Dupuis formula and the exponential hypercontractivity in the Gaussian space
This paper concerns a variational representation formula for Wiener functionals. Let B={Bt}t≥0 be a standard d-dimensional Brownian motion. Boué and Dupuis (1998) showed that, for any bounded measurable functional F(B) of B up to time 1, the expectation EeF(B) admits a variational representation in terms of drifted Brownian motions. In …