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

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

2007-09-04

arxiv.org/abs/0709.0402v1

Mathematics

Probability

Accept\'e conditionnelement par Stochastic processes and their applications

Scientific paper

Through a regularization procedure, few approximation schemes of the local time of a large class of one dimensional processes are given. We mainly consider the local time of continuous semimartingales and reversible diffusions, and the convergence holds in ucp sense. In the case of standard Brownian motion, we have been able to determine a rate of convergence in $L^2$, and a.s. convergence of some of our schemes.

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