Random Flights and Statistics for Diffusion Processes
Seminario di Dipartimento, del prof. Alessandro De Gregorio
In the first part of the talk, we introduce some types of evolutionary systems that change their mode of evolution following a stochastic mode. In particular, we deal with the so-called Random Flights which are often described by the motion of a particle whose velocity performs jumps of random length at random times. We review the results concerning the features of these stochastic processes. Moreover, the connection between Random Flights and nonlinear diffusion models is also discussed.
In the second part of the talk, we deal with some parametric inference problems for stochastic differential equations observed at discrete times. In particular, we focus our attention to hypothesis testing and regularized estimation for diffusion processes. Furthermore, we discuss the asymptotic properties of the introduced statistics.