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Variational calculus for diffusions
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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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Cited by 1 Pith paper
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Strong solutions of SDE's with rough coefficients
A Brownian SDE with merely measurable, Markovian drift is claimed to have a unique strong solution and H-C regular solution map whenever its Girsanov density has a finite L^{1+ε} moment.
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