LOCALIZABLE MOVING AVERAGE SYMMETRIC STABLE AND MULTISTABLE PROCESSES

We study a particular class of moving average processes that possess a property called localizability. This means that, at any given point, they admit a tangent process, in a suitable sense. We give general conditions on the kernel g defining the moving average which ensures that the process is localizable and we characterize the nature of the associated tangent processes. Examples include the reverse Ornstein-Uhlenbeck process and the multistable reverse Ornstein-Uhlenbeck process. In the latter case, the tangent process is, at each time t, a Levy stable motion with stability index possibly varying with t. We also consider the problem of path synthesis, for which we give both theoretical results and numerical simulations.