This note presents a method based on Feynman-Kac semigroups for logarithmic Sobolev inequalities. It follows the recent work of Bonnefont and Joulin intertwining relations diffusion operators, formerly used spectral gap inequalities, related to perturbation techniques. In particular, it goes beyond Bakry-Émery criterion allows investigate high-dimensional effects optimal constant. The is illust...

The existing formulations of the Schrödinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend the framework to encompass singular pot...

We discuss the so-called Schrödinger problem of deducing the microscopic (basically stochastic) evolution that is consistent with given positive boundary probability densities for a process covering a finite fixed time interval. The sought for dynamics may preserve the probability measure or induce its evolution, and is known to be uniquely reproducible, if the Markov property is required. Feyn...

Suppose that α ∈ (0, 2) and that X is an α-stable-like process on R d. Let µ be a signed measure on R d belonging to the class K d,α and A µ t be the continuous additive functional of X associated with µ. In this paper we show that the Feynman-Kac semigroup {T µ t : t ≥ 0} defined by T µ t f (x) = E x e −A µ t f (X t) has a density q µ and that there exist positive constants c 1 , c 2 , c 3 , c...