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arXiv · 1607.05488

Variational calculus for diffusions

Kévin Hartmann
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Abstract

We expand the classic variational formulation of $-\log\mathbb{E}\left[e^{-f}\right]$ to the case where f depends on a diffusion, and not only a on Brownian motion, while decreasing the integrability hypothesis on f. We also give an entropic characterisation of the invertibility of a perturbation of a diffusion and discuss the attainability of the infimum in the aforementioned variational formulation.

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Kévin Hartmann. 2016-07-19. Variational calculus for diffusions. https://arxiv.org/abs/1607.05488

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