Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions

Abstract

For one-dimensional diffusions on the half-line, we study a specific type of conditioning to avoid zero. We introduce supermartingales defined via concave functions with respect to the scale function. A conditioning is formulated through the exit times of the supermartingale, and its existence is shown. We also investigate the absolute continuity relations of the limit laws at time infinity.

38 pages