Local time approximation in parameter estimation for skew-sticky diffusions

In this seminar we first describe a class of one-dimensional Markov processes with continuous sample paths which shows singular behavior at a point, let us say barrier. The barrier is semi-permeable ou semi-reflecting, or sticky, or playes the role of a threshold which makes the behavior change above and below. Starting from an observation of a trajctory, it is natural to try to detect these behaviors, which are encoded in some parameters. The approximation of the local time (think of the time spent on an infinitesimal interval around the barrier) allows us to construct estimators for the parameters and to show asymptotic mixed normality properties. This talk is partially based on a joint work with A. Anagnostakis