Approximation via regularization of the local time of semimartingales and Brownian motion

Through a regularization procedure, a few schemes for approximation of the local time of a large class of continuous semimartingales and reversible diffusions are given. The convergence holds in the ucp sense. In the case of standard Brownian motion, we have been able to bound the rate of convergence in L2, and to establish the a.s. convergence of some of our schemes.