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 δ ∈ ]0; 2[ which are reflected at 1.
Cite this article
Christophe Profeta, Penalization of a Positively Recurrent Diffusion by an Exponential Function of its Local Time. Publ. Res. Inst. Math. Sci. 46 (2010), no. 3, pp. 681–718DOI 10.2977/PRIMS/22