Antoine Ayache

Professor
Laboratoire Paul Painlevé
Unité Mixte de Recherche CNRS 8524, Université Lille 1
E-mail: Antoine.Ayache@math.univ-lille1.fr
Curriculum vitae: click here

Bureau / Office: 213 bâtiment M3
Téléphone / Phone: (33) 3 20 43 42 27
Adresse Postale / Postal Address:
Laboratoire Paul Painlevé
Université Lille 1
Bât. M2
Villeneuve d'Ascq 59655 Cedex, FRANCE

Main research topics:
- Sample path behavior of multifractional and anisotropic fields
- Statistical inference for multifractional and anisotropic fields
- Random series
- Local times
- Fractal dimensions

Some talks:
- Talk at the Colloquium of Mathematics of the laboratory LAMFA at the University of Picardie Jules Verne (Amiens, October 2015) Erratic random functions: the concept of local nondeterminism and the study of Harmonizable Fractional Stable Field
- Talk at the conference "Stochastic Analysis and Applications" (Bucharest, December 2014) and at the SAMM seminar of the University Paris 1 (May 2015) Uniformly and strongly consistent estimation for the Hurst function of a Linear Multifractional Stable Motion
- Talk at a meeting of the Research Group (GDR) "Multifractal Analysis" (September 2013) and at the Probability and Statistics Seminar of the University Lille 1 (Septembrer 2014): Harmonizable Fractional Stable Fields: Local Nondeterminism and Joint Continuity of the Local Times
- Talk at the Computational Analysis Seminar of the Vanderbilt University (April 2012) and at the Stochastics Seminar of the University of Utah (August 2012): Optimal Series Representations of Continuous Gaussian Random Fields
- Talk at the Conference "Fractals and Related Fields II" (June 2011): Continuous Gaussian multifractional processes with random pointwise Holder regularity
- Two days seminar at the University of Cassino (December 2010); First talk: From Fractional Brownian Motion to Mutifractional Brownian Motion ; Second talk: ; From Mutifractional Brownian Motion to Generalized Mutifractional Brownian Motion; Thrid talk: Identification of the pointwise Holder exponent of Generalized Mutifractional Brownian Motion ; Fourth talk: From Mutifractional Brownian Motion to Multifractional Process with Random Exponent
- Talk at the Stochastic Analysis Seminar of the University of Oxford (February 2010): Fractional and Multifractional fields from a wavelet point of view
- Talk at the conference "Small Deviation Probabilities and Related Topics", St. Peterburg (September 2005): Rate optimality of wavelet series expansions of Fractional Brownian Motion
- Talk (in french) at the meeting "Rencontre Anciens Nouveaux" at Ambeteuse (November 2004): Une petite excursion en géometrie fractale

Main teaching activities:
- I taught the following mini-course at National Taiwan University (December 2009) and at the Faculty of Sciences of Monastir in Tunisia (January 2011): Wavelets and Fractional Processes
- I gave an introductory course on "Fractional and Multifractional Processes" at Wuhan University in China (September 2010) and at the Faculty of Sciences of Monastir in Tunisia (October 2010)
- From 2005-2006 to 2008-2009, I gave a course on "Functional Analysis" in master 2 degree of research in Applied Mathematics. Here are (in french) the examinations and their corrections: January 2006 ; April 2006 ; January 2007 ; April 2007 ; December 2007 ; December 2008 ; Orals March 2008, February 2009 and March 2009 .
- From 2010-2011 to 2013-2014, I gave a course on "Stochastic Processes" in master 2 degree of research in Applied Mathematics. Here are (in french) some notes on the first part of the course, the examinations and other documents: "Loi de probabilité d'un processus et sujets connexes" (notes de cours) ; Written exam 2011 ; Oral exam 2011 (number 1) ; Oral exam 2011 (number 2) ; Homework 2012 ; Correction of the homework 2012 ; Written exam 2012 ; Correction of the written exam 2012 ; Homework 2013 ; Correction of the homework 2013 ; Written exam 2013 ; Correction of the written exam 2013 ; Oral exam 2013 (number 1) ; Oral exam 2013 (number 2) ; Written exam 2014 ; Correction of the written exam 2014 .
- In the present year 2015-2016, I give a course on "Ito stochastic integrals" in master 2 degree of research in Applied Mathematics. I will also give this same course on the next year.
- I teach "Probability and Statistics" at all levels at the IAE de Lille http://www.iae.univ-lille1.fr/. Here is (in french) an elementary course in Descriptive Statistics .


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