On h-transforms of one-dimensional diffusions stopped upon hitting zero

Abstract

For a one-dimensional diffusion on an interval for which 0 is the regularreflecting left boundary, three kinds of conditionings to avoid zero are studied. The limit processes are h-transforms of the process stopped upon hitting zero, where h’s are the ground state, the scale function, and the renormalized zero-resolvent. Several properties of the h-transforms are investigated.