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

Blandine Berard Bergery (1) , Pierre P. Vallois (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques

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.

Mots clés: local time; stochastic integration by regularization; quadratic variation; rate of convergence; stochastic Fubini's theorem

Domaines: Probabilités [math.PR]

Blandine Berard Bergery, Pierre P. Vallois. Approximation via regularization of the local time of semimartingales and Brownian motion. Stochastic Processes and their Applications, 2008, 118, pp.2058-2070. ⟨10.1016/j.spa.2007.12.002⟩. ⟨hal-00169518⟩