Section: New Results

Self-stabilizing processes

Participants : Xiequan Fan, Jacques Lévy Véhel.

In collaboration with K. Falconer, University of St Andrews.

Self-stabilizing processes are càdlàg processes whose local intensiy of jumpd depend on amplitude. We have investigated two paths to define such processes. The first one is based on a modification of the celebrated Lévy construction of Brownian motion.

The second one starts from a stochastic differentiel equation, and allows one to build Markov processes, a useful feature in applications such as financial modelling [40] , [41] .