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How rich is the class of multifractional Brownian motions? (English) Zbl 1094.60024

The authors study two types of multifractional Brownian motion processes introduced by Peltier and Lévy-Vehel (1995) and A. Benassi, S. Jaffard and D. Roux [Rev. Mat. Iberoam. 13, No. 1, 19–90 (1997; Zbl 0880.60053)]. It is shown that these two types of processes have different correlation structures when their self-similarity parameters depend on time and are non-constants. This result contradicts with results in the literature on similarity of these two types of processes. The authors investigate the general class of multifractional Brownian motion processes, which includes the mentioned two types.

MSC:

60G15 Gaussian processes
60G18 Self-similar stochastic processes
60K99 Special processes

Citations:

Zbl 0880.60053
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References:

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