Multifractal process; Law of the iterated logarithm; Brownian motion
Abstract :
[en] We give a construction of a multifractal process with prescribed Hölder exponents starting from the Lévy–Ciesielski construction of a Brownian motion. We also show that this method preserves the law of the iterated logarithm.
Disciplines :
Mathematics
Author, co-author :
Kleyntssens, Thomas ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Ayache, A., Bertrand, P., A process very similar to multifractional Brownian motion. Recent Developments in Fractals and Related Fields, 2010, Birkhäuser, Boston, 311–326.
Ayache, A., Taqqu, M., Rate optimality of wavelet series approximations of fractional Brownian motion. J. Fourier Anal. Appl. 9 (2003), 451–471.
Bhattacharya, R., Waymire, E.C., Kolmogorov's extension theorem and Brownian motion. A Basic Course in Probability Theory, 2016, Springer International Publishing, 167–178.
Chatterjee, S., Superconcentration and Related Topics. 2014, Springer.
Daoudi, K., Lévy Véhel, J., Meyer, Y., Construction of continuous functions with prescribed local regularity. Constr. Approx. 14:3 (1998), 349–385.
Faber, G., Ueber die Orthogonalfunktionen des Herrn Haar. Jahresber. Deutsch. Math. Verein. 19 (1910), 104–112.
Khintchine, A., Über einen satz der wahrscheinlichkeitsrechnung. Fund. Math. 6 (1924), 9–20.
Kleyntssens, T., New Methods for Signal Analysis: Multifractal Formalisms based on Profiles. From Theory to Practice. (Ph.D. thesis), 2019, Université de Liège.
Meyer, Y., Sellan, F., Taqqu, M., Wavelets, generalized white noise and fractional integration: the synthesis of fractional Brownian motion. J. Fourier Anal. Appl. 5 (1999), 465–494.
Schauder, J., Eine eigenschaft des haarschen orthogonalsystem. Math. Z. 28 (1928), 317–320.
