A criteria of strong H-differentiability
We give a criteria for a Malliavin differentiable function to be strongly H-differentiable.
math.PR↗
arXiv subjects
Kévin Hartmann
Publications and source records attributed to Kévin Hartmann.
Variational calculus for diffusions
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.
math.PR↗
A general framework for variational calculus on Wiener space
We provide a framework to derive a variational formulation for $-\log\mathbb{E}_ν\left[e^{-f}\right]$ for a large class of measures $ν$. We use a family of perturbations of the identity $(W^u)$ whose invertibility we characterize thanks to entropy. This yields results of strong existence for various stochastic differential equations. We also discuss the attainability of the infimum in the variational formulation and we derive a Prékopa-Leindler theorem for the measure $ν$.
math.PR↗
Variational calculus on Wiener space with respect to conditional expectations
We give a variational formulation for $-\log\mathbb{E}_ν\left[e^{-f}|\mathcal{F}_t\right]$ for a large class of measures $ν$. 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.
math.PR↗