THE EXCURSION DECOMPOSITION OF THE PATHS OF A CLASS OF DIFFUSIONS

In this paper, the excursion decomposition of the paths of a cerlain class of diffusions is carried out. Using Maisonneuve’s exit system, we obtain the concrete form of the characteristic measure n of the respective Poisson point processes in terms of the transition density functions of the diffusions. As an example, we give a stochastic integral version of Ornstein-Uhlenbeck Processes starting from zero. Finally, although it is known, an invariant measure of these processes is obtained via Getoor’s method.