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arXiv · 1607.05555

Variational calculus on Wiener space with respect to conditional expectations

Kévin Hartmann
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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 Pr\'ekopa-Leindler theorem for conditional expectations.

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Kévin Hartmann. 2016-07-19. Variational calculus on Wiener space with respect to conditional expectations. https://arxiv.org/abs/1607.05555

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