Non-Autonomous Kato Classes and Feynman-Kac Propagators

Classes of time-dependent measures, non-homogeneous Markov processes, and Feynman-Kac propagators

“…We discuss the strong continuity of propagators on the space L r , the (L r − L q )-smoothing property, and various versions of the Feller property. More results concerning the similarities in the behaviour of semigroups (propagators) and their perturbations by potentials can be found in [1,2,3,4,5,6,7,14,16,17,18,19,20,21,22,32,34,37,38,39,40,42,43,44,45]. In Section 8 we establish that the Feller property, the Feller-Dynkin property, and the BUC-property are inherited by Feynman-Kac propagators from free propagators under additional restrictions on functions and time-dependent measures generating Feynman-Kac propagators.…”

“…This result (Theorem 2.2 below) was first formulated without proof in [19]. The proof appeared in the CRM preprint [20].…”

Forward-Backward Stochastic Differential Equations Generated by Bernstein Diffusions

“…(a) The process (A τ , B τ , C τ ) τ ∈[0,T ] is the unique solution to the forwardbackward system whose stochastic differential equations are of the form (3) and (4) with f and g given by (10) and (11), respectively. The uniqueness is meant as uniqueness in law.…”

The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)

“…Various books have already been published, where Bernstein reciprocal processes play a major role. We mention only two recent ones besides [9]: [27], [57]. In each theoretical or experimental scientific situation where it seems natural to provide a pair of arbitrary initial and final probability densities, for a given system driven by any "Hamiltonian" H, time reversible processes like those described here should arise.…”