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Localisable moving average stable and multistable processes

Research paper by Kenneth Falconer, Ronan Le Guével, Jacques Lévy-Véhel

Indexed on: 25 Jun '09Published on: 25 Jun '09Published in: Mathematics - Probability



Abstract

We study a particular class of moving average processes which possess a property called localisability. 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 localisable 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 L\'evy 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.