Variational calculus on Wiener space with respect to conditional expectations

Abstract

We give a variational formulation for $-\log {\mathbb{E}}_{\nu }\left[e^{-f}|{\mathcal{F}}_t\right]$ for a large class of measures $\nu$. We give a refined entropic characterization of the invertibility of some perturbations of the identity. We also discuss the attainability of the infimum in the variational formulation and obtain a Prékopa-Leindler theorem for conditional expectations.

arXiv admin note: substantial text overlap with arXiv:1607.05542, arXiv:1607.05488

References in corpus (1)

• A general framework for variational calculus on Wiener space