Stochastic 2-microlocal analysis
| dc.creator | Herbin, Erick | |
| dc.creator | Lévy-Véhel, Jacques | |
| dc.date | 2005-04-27 | |
| dc.date | 2008-11-22 | |
| dc.date.accessioned | 2026-07-07T10:19:51Z | |
| dc.date.available | 2026-07-07T10:19:51Z | |
| dc.description | A lot is known about the Hölder regularity of stochastic processes, in particular in the case of Gaussian processes. Recently, a finer analysis of the local regularity of functions, termed 2-microlocal analysis, has been introduced in a deterministic frame: through the computation of the so-called 2-microlocal frontier, it allows in particular to predict the evolution of regularity under the action of (pseudo-) differential operators. In this work, we develop a 2-microlocal analysis for the study of certain stochastic processes. We show that moments of the increments allow, under fairly general conditions, to obtain almost sure lower bounds for the 2-microlocal frontier. In the case of Gaussian processes, more precise results may be obtained: the incremental covariance yields the almost sure value of the 2-microlocal frontier. As an application, we obtain new and refined regularity properties of fractional Brownian motion, multifractional Brownian motion, stochastic generalized Weierstrass functions, Wiener and stable integrals. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504551 | |
| dc.identifier | http://arxiv.org/abs/math/0504551 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174662 | |
| dc.subject | Probability | |
| dc.subject | 62G05; 60G15; 60G17; 60G18 | |
| dc.title | Stochastic 2-microlocal analysis | |
| dc.type | text |