Antoine Ayache

Professor
Laboratoire Paul Painlevé
Unité Mixte de Recherche CNRS 8524, Université de Lille
E-mail: antoine.ayache@univ-lille.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
Cité Scientifique
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 CIRM (Marseille (France), February 2016) and at the workshop Fractality and Fractionality (Lorentz center Leiden (Netherlands), May 2016) and at the 8th International Conference on Lévy Processes (Angers (France), July 2016) Stationary increments harmonizable stable fields: upper estimates on path behaviour
- 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 .
- From 2015-2016 to 2017-2018, I gave a course on "Ito Stochastic Integrals" in master 2 degree of research in Applied Mathematics. Here are (in french) the examinations: March 2016 ; March 2017 ; June 2017 ; March 2018 ; Oral May 2018 .
- 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 and Computational Probability .


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