Ayache, Antoine; Lévy Véhel, Jacques 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]. Reviewer: Esko Valkeila (Helsinki) Cited in 2 ReviewsCited in 18 Documents MSC: 60G15 Gaussian processes 60G18 Self-similar stochastic processes Keywords:generalized multifractional Brownian motion; local self-similarity PDFBibTeX XMLCite \textit{A. Ayache} and \textit{J. Lévy Véhel}, in: Fractals: Theory and applications in engineering. London: Springer. 17--32 (1999; Zbl 0964.60046)