Skip to Main content Skip to Navigation
Journal articles

Stochastic 2 micro-local analysis

Abstract : 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 otained: 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [23 references]  Display  Hide  Download

https://hal.inria.fr/inria-00538965
Contributor : Lisandro Fermin <>
Submitted on : Tuesday, November 23, 2010 - 3:56:05 PM
Last modification on : Wednesday, April 8, 2020 - 4:04:21 PM
Long-term archiving on: : Thursday, February 24, 2011 - 2:38:54 AM

File

reg-SPArevised2.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Erick Herbin, Jacques Lévy Véhel. Stochastic 2 micro-local analysis. Stochastic Processes and their Applications, Elsevier, 2009, 119 (7), pp.2277-2311. ⟨10.1016/j.spa.2008.11.005⟩. ⟨inria-00538965⟩

Share

Metrics

Record views

467

Files downloads

411