Localisable moving average symmetric stable and multistable processes

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 Lévy 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.
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Stochastic Models, INFORMS (Institute for Operations Research and Management Sciences), 2009, 25 (4), pp.648-672. 〈10.1080/15326340903291321〉
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Kenneth Falconer, Ronan Le Guével, Jacques Lévy Véhel. Localisable moving average symmetric stable and multistable processes. Stochastic Models, INFORMS (Institute for Operations Research and Management Sciences), 2009, 25 (4), pp.648-672. 〈10.1080/15326340903291321〉. 〈inria-00538980〉

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