Speaker: Sveinn Olafsson, Visiting Assistant Professor, UC Santa Barbara
Since the work of Page in the 1950s, the problem of detecting an abrupt change in the distribution of stochastic processes has received a great deal of attention. There are two main formulations of such problems: A Bayesian approach where the change-point is assumed to be random, and a min-max approach under which the change-point is assumed to be fixed but unknown. In both cases, a deep connection has been established to variations of the widely used CUSUM procedure, but results for processes with jumps are still scarce, while the practical importance of such processes has escalated. In this talk we consider change-point detection problems for processes with independent and stationary increments, i.e. Levy processes, as well as some important extensions, such as to processes with a dependence structure, and to the case of distributional uncertainty.