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Journal Articles Stochastic Models Year : 2009

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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Dates and versions

inria-00538980 , version 1 (23-11-2010)

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Kenneth J. Falconer, Ronan Le Guével, Jacques Lévy Véhel. Localisable moving average symmetric stable and multistable processes. Stochastic Models, 2009, 25 (4), pp.648-672. ⟨10.1080/15326340903291321⟩. ⟨inria-00538980⟩
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