Penalization of a Positively Recurrent Diffusion by an Exponential Function of its Local Time

Abstract

Using Krein's theory of strings, we penalize here a large class of positively recurrent diffusions by an exponential function of their local time. After a brief study of the processes so penalized, we show that on this example the principle of penalization can be iterated, and that the family of probabilities we get forms a group. We conclude by an application to Bessel processes of dimension $\delta \in ]0;2[$ which are reflected at $1$.