Regularity and identification of Generalized Multifractional Gaussian Processes

Antoine Ayache (1) , Albert Benassi (2) , Serge Cohen (1) , Jacques Lévy Véhel (3)

1 LSP - Laboratoire de Statistique et Probabilités
2 LaMP - Laboratoire de météorologie physique
3 FRACTALES - Fractals, complex models and artificial evolution

In this article a class of multifractal processes is introduced, called Generalized Multifractional Gaussian Process (GMGP). For such multifractional models, the Hurst exponent on the celebrated Fractional Brownian Motion is replaced by a function, called the multifractional function, which may be irregular. The main aim of thi paper is to show how to identify irregular multifractional functions in the setting of GMGP. Examples of discontinuous multiractional functions are also given.

Domaines: Probabilités [math.PR]

Antoine Ayache, Albert Benassi, Serge Cohen, Jacques Lévy Véhel. Regularity and identification of Generalized Multifractional Gaussian Processes. Lecture Notes in Mathematics, 2004, Séminaire de Probabilités XXXVIII, 1857, pp.290-312. ⟨10.1007/978-3-540-31449-3_20⟩. ⟨inria-00576446⟩