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Multifractional, multistable, and other processes with prescribed local form

Abstract : We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional -stable processes, and multistable processes, that is processes that are locally \alpha(t)-stable but where the stability index \alpha(t) varies with t. In particular we construct multifractional multistable processes, where both the local self-similarity and stability indices vary.
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Submitted on : Tuesday, November 23, 2010 - 5:16:24 PM
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Kenneth J. Falconer, Jacques Lévy Véhel. Multifractional, multistable, and other processes with prescribed local form. Journal of Theoretical Probability, Springer, 2009, 22 (2), pp.375-401. ⟨10.1007/s10959-008-0147-9⟩. ⟨inria-00539033⟩

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