Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

This work is concerned with a class of Schrödinger process with unbounded potentials : a variant of Jamison's theorem is given without the assumption of continuity and of everywhere strict positivity of q. It associates with Jamison's data (q, Pa, Pb), the Csiszar's projection Q* of a reference measure R* on a set E(Pa, Pb) of probability measures with marginals Pa, Pb. Existence of a solution to the corresponding Schrödinger's system, construction of the Schrödinger's bridge and variational characterisation of Schrödinger process are established.