The differentiation of hypoelliptic diffusion semigroups

The Differentiation of Hypoelliptic Diffusion Semigroups

Basic derivative formulas are presented for hypoelliptic heat semi-groups and harmonic functions extending earlier work in the elliptic case. Following the approach of 15], emphasis is placed on developing integration by parts formulas at the level of local martingales. Combined with the optional sampling theorem, this turns out to be an eecient way of dealing with boundary conditions, as well ...

new semigroup compactifications via the enveloping semigroups of associated flows

this thesis deals with the construction of some function algebras whose corresponding semigroup compactification are universal with respect to some properies of their enveloping semigroups. the special properties are of beigan a left zero, a left simple, a group, an inflation of the right zero, and an inflation of the rectangular band.

Estimates for the Derivative of Diffusion Semigroups

Let {Pt}t≥0 be the transition semigroup of a diffusion process. It is known that Pt sends continuous functions into differentiable functions so we can write DPtf. But what happens with this derivative when t → 0 and P0f = f is only continuous ?. We give estimates for the supremum norm of the Fréchet derivative of the semigroups associated with the operators A + V and A + Z · ∇ where A is the ge...

Hypoelliptic Diffusion and Human Vision: A Semidiscrete New Twist

Hypercontractivity for perturbed diffusion semigroups

μ being a nonnegative measure satisfying some Log-Sobolev inequality, we give conditions on F for the Boltzmann measure ν = eμ to also satisfy some Log-Sobolev inequality. This paper improves and completes the final section in [6]. A general sufficient condition and a general necessary condition are given and examples are explicitly studied. Résumé. μ étant une mesure positive satisfaisant une ...