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Generalized multifractional Brownian motion: Definition and preliminary results. (English) Zbl 0964.60046

Dekking, Michel (ed.) et al., Fractals: Theory and applications in engineering. London: Springer. 17-32 (1999).
Multifractional Brownian motion is a generalization of fractional Brownian motion, where the constant self-similarity parameter \(H\) is allowed to be a smooth function \(H(t)\). The authors generalize this notion to a case, where the parameter \(H(t)\) is not necessarily a smooth function, but it can belong to a larger class, which is obtained as a limit of Hölder continuous functions. After giving the basic definition of generalized multifractional Brownian motion the authors study its regularity and self-similarity properties.
For the entire collection see [Zbl 0936.00006].

MSC:

60G15 Gaussian processes
60G18 Self-similar stochastic processes
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