Curriculum Vita
Last name: AYACHE First name: Antoine Date of birth: 09/22/1969 Nationality: French
Personal situation: Single
Professional address: Bˆat. M2, Univ. Lille 1, 59655 Villeneuve d’Ascq, France Phone number: (33)3.20.43.42.27
Fax number: (33)3.20.43.43.02
E-mail : Antoine.Ayache@math.univ-lille1.fr
CURRENT POSITION
Professor “Professeur deuxi`eme classe” in Mathematics, I was recruited by the University Lille 1 (Lille, France)the 09/1/2004 at “Laboratoire Paul Painlev´e” (the research unit in Mathematics).
→Since October 2004, I receive a bonus for my supervision and research activities “Prime d’Encadrement Doctoral et de Recherche”.
PREVIOUS POSITIONS
- Assistant Professor in Mathematics “Maˆıtre de Conf´erences”from 09/1/1999 to 08/31/2004 at the LSP (the research unit in Stastistics and Probability) of the Uni- versity Paul Sabatier (Toulouse, France).
→ From 09/1/2003 to 08/31/2004, I was on a research mission at the CNRS at the the research unit CMLA (Center of Mathematics and Their Applications) of ENS Cachan.
- Full time ATER (this is a french equivalent to a post-doc position including teach- ing responsabilities), at the research unit CEREMADE (Reasearch Center of Mathematics of Decision) of the University Paris Dauphine, from 09/1/97 to 08/31/99.
- Associate reseacher within the Fractal project at INRIA (National Re- search Institut in Computer Science and Automatics) Rocquencourt, from 01/1/99 to 08/31/99.
- Phd fellowship (from 10/1/94 to 08/31/97).
DIPLOMA
- Habilitation Thesis (this is the required diploma in France for applying to a po- sition of associate professor).
Title: Beyond Fractional Brownian Motion. Date: 12/15/03. Place: Univer- sity Paul Sabatier. Research director: Professor Y. Meyer. President of the jury:
Professor C. Houdr´e. Referees: Professors K.J. Falconer, S. Jaffard and M.A.
Lifshits. Other members of the jury: Professors A. Bonami and M. Ledoux.
- PhD Thesis in Applied Mathematics (passed with distinction).
Title: Non separable, multivariate, compactly supported, othonormal wavelet bases with an arbitrary regularity. Date: 12/3/97. Place: University Paris Dauphine. Supervisor: Professor Y. Meyer. President of the jury: Professor P.
Le Tallec. Referees: Professors I. Daubechies, A. Cohen and P.G. Lemari´e- Rieusset.
- “DEA” in Pure Mathematics (post-graduate qualification in Pure Mathematics which is a prerequisite for PhD candidates) (passed with distinction).
Date: June 94. Place: University Paris-Sud Orsay.
We had to pass 2 courses and write a DEA’s thesis. In order to acquire a double compe- tence: in Analysis (Harmonic Analysis and Functional Analysis) and Algebra (basic Algebraic Geometry), I passed 5 courses and wrote my DEA’s thesis.
- “Grande ´ecole” ENSAE (This is a college of university level specializing in pro- fessional training in Statistics and Economics. Its students are highly selected). I obtained my degree in June 93.
- “DEA” in Stochastic Modeling Economics and Finance.
Place: University Paris VII. In order to strengthen my knowledge of Probabil- ity, Statistics and their applications, I passed half of the required courses of this
“DEA”, while working on my PhD Thesis. These courses concern stochastic calculus and methods for evaluating options in financial markets.
- Master’s degree in Pure Mathematics (passed with distinction).
Date: June 91. Place: University Paris VI.
Courses: Topology, Functional Analysis, Commutative Algebra, Quadratic forms & clas- sical groups.
- Undergraduate studies
• third year: “Licence” in Applied Mathematics(passed with distinction).
Date: June 90. Place: University Paris Dauphine.
Courses: Probability, Statistics, Computer Science, Automatics, Differential Sys- tems, Hilbertian Analysis, Measure Theory and Integration, Metric Spaces.
• first and second year: “DEUG” in Applied Mathematics and Social Sciences (passed with distinction).
Date: June 89. Place: University Paris Dauphine.
- “Baccalaur´eat”, Mathematics and Physics orientation(secondary school ex- amination qualifying for entry to university) (passed with distinction).
Date: July 87.
MAIN RESEARCH TOPICS
- Multifractional Processes, self-similarity and H¨older regularity:
→ Generalized Multifractional Brownian Motions,
→ Multifractional Processes with random exponents.
- Statistical inference for Multifractional and Anisotropic fields:
→ H¨older exponents and generalized quadratic variations,
→ H¨older exponents and wavelet coefficients,
→ Central Limit Theorems.
- Random series:
→ Wavelet type series and uniform results on the regularity,
→ Operator theory and optimal random series decompositions.
- Local times:
→ Existence, joint continuity and H¨older conditions.
- Fractal dimensions:
→ Graphs, images and level sets.
- Lifetime Value in Relationship Marketing:
→ Stochastic modelling.
LIST OF PUBLICATIONS IN MATHEMATICS
1) Ayache A. ; Continuous Gaussian multifractional processes with random pointwise H¨older regularity. Journal of Theoretical Probability to appear.
2) Ayache A., Hamonier H. ; Linear fractional stable motion: a wavelet estimator of the α parameter. Statistics and Probability Letters to appear.
3) Ayache A., Shieh N.R., Xiao Y. ; Multiparameter multifractional Brownian motion:
Local nondeterminism and joint continuity of the local times. Annales de l’Institut Henri Poincar´e (B) Probabilit´es et Statistiques47:1029-1054 (2011).
4) Ayache A., Peng P. ; Stochastic volatility and Multifractional Brownian Motion.
Stochastic Differential Equations and Processes. Spinger-Verlag eds Zili and Filatova 211–238 (2011).
5) Ayache A., Bertrand P. ; Discretization error of wavelet coefficient for fractal like process. Advances in Pure and Applied Mathematics 2:297-321 (2011).
6) Lopes R., Ayache A., Makni N., Puech P., Villers A., Mordon S., Betrouni N ; Prostate cancer characterization on MR images using fractal features. Medical Physics 38:83-95 (2011).
7) Ayache A., Bertrand P. ; A process very similar to multifractional Brownian motion Fractal and Related Fields. Birkh¨auser eds Barral and Seuret 311-326 (2010).
8) Ayache A., Jaffard S. ; H¨older exponents of arbitrary functions. Revista Matematica Iberoamericana 26:1:77-89 (2010).
9) Ayache A., Linde W. ; Series Representations of Fractional Gaussian Processes by Trigonometric and Haar Systems. Electronic Journal of Probability 94:2691-2719 (2009).
10) Ayache A., Roueff F., Xiao Y. ; Linear Fractional Stable Sheets: Wavelet expansion and sample path properties. Stochastic Processes and their Applications 119:1168-1197 (2009).
11) Ayache A., Linde W. ; Approximation of Gaussian Random Fields: General Re- sults and Optimal Wavelet Representation of the L´evy Fractional Motion. Journal of Theoretical Probability 21:69-96 (2008).
12) Ayache A., Tzvetkov N. ; Lp properties for Gaussian random series. Transactions of the American Mathematical Society360:4425-4439 (2008).
13) Ayache A., Wu D., Xiao Y. ; Joint Continuity of the Local Times of Fractional Brownian Sheets. Annales de l’Institut Henri Poincar´e (B) Probabilit´es et Statistiques 44:4:727-748 (2008).
14) Ayache A., Roueff F., Xiao Y. ; Joint Continuity of the Local Times of Linear Fractional Stable Sheets. Comptes Rendus de l’Acad´emie des Sciences de Paris,344:I:635- 640 (2007).
15) Ayache A., Roueff F., Xiao Y. ; Local and Asymptotic Properties of Linear Frac- tional Stable Sheets. Comptes Rendus de l’Acad´emie des Sciences de Paris,344:I:389-394 (2007).
16) Ayache A., Jaffard S., Taqqu M.S. ; Wavelet construction of Generalized Multi- fractional Processes. Revista Matematica Iberoamericana 23:1:327-370 (2007).
17) Ayache A., Bonami A., Estrade A. ; Identification and wavelet decomposition of anisotropic Gaussian fields. More Progresses in Analysis. Proceedings of the 5th Interna- tional ISAAC Congress. World Scientific eds Begehr and Nicolosi 441-450 (2009).
18) Ayache A., Bertrand P., L´evy V´ehel J. ; A central limit theorem for the quadratic variations of the step fractional Brownian motion. Statistical Inference for Stochastic Processes 10:1:1-27 (2007).
19) Ayache A., Heinrich P., Marsalle L., Suquet Ch. ; Holderian random functions.
Fractals in Engineering· New Trends in Theory and Applications. Springer-Verlag eds L´evy V´ehel and Lutton 33-56 (2005).
20) Ayache A., Xiao Y. ; Asymptotic Growth Properties and Hausdorff dimensions of Fractional Brownian Sheets. Journal of Fourier Analysis and Applications 11:4:407-439 (2005).
21) Ayache A., Taqqu M.S. ; Multifractional Processes with Random Exponent. Pub- licaciones Matem`atiques49:459-486 (2005).
22) Ayache A. ; Hausdorff dimension of the graph of the Fractional Brownian Sheet.
Revista Matematica Iberoamericana 2:20:395-412 (2004).
23) Ayache A., L´evy V´ehel J. ; Identification of the pointwise H¨older exponent of Generalized Multifractional Brownian Motion. Stochastic Processes and their Applications 111:119-156 (2004).
24) Ayache A., Benassi A., Cohen S., L´evy V´ehel J. ; Regularity and identification of Generalized Multifractional Gaussian Process. S´eminaire de Probabilit´es XXXVIII:290- 312 (2005).
25) Ayache A., Taqqu M.S. ; Rate optimality of wavelet series approximations of fractional Brownian motion. Journal of Fourier Analysis and Applications 9:5:451-471 (2003).
26) Ayache A., Roueff F. ; A Fourier formulation of the Frostman criterion for random graphs and its application to wavelet series. Letter to the editor Applied and Computa- tional Harmonic Analysis 14:75-82 (2003).
27) Ayache A., L´eger S., Pontier M. ; Les ondelettes `a la conquˆete du Drap Brownien Fractionnaire. Comptes Rendus de l’Acad´emie des Sciences de Paris. 335, I, 1063-1068 (2002).
28) Ayache A. ; The Generalized Multifractional Field: A nice tool for the study of the Generalized Multifractional Brownian Motion. Journal of Fourier Analysis and Applications 8:581-601 (2002).
29) Ayache A., L´eger S., Pontier M. ; Drap Brownien Fractionnaire. Potential Analysis 17:31-43 (2002).
30) Ayache A. ; Du mouvement brownien fractionnaire au mouvement brownien mul- tifractionnaire (article de synth`ese). Technique et science informatiques 20:9:1133-1152 (2001).
31) Ayache A., L´evy V´ehel J. ; Processus `a r´egularit´e locale prescrite. Comptes Rendus de l’Acad´emie des Sciences de Paris 333, I, 233-238, (2001).
32) Ayache A. ; Some methods for constructing non separable, orthonormal, compactly supported wavelet bases. Lettre `a l’´editeurApplied and Computational Harmonic Analysis 10:99-111 (2001).
33) Ayache A., Cohen S., L´evy V´ehel J. ; The covariance structure of multifractional Brownian motion. Proceedings IEEE-ICASSP 6:3810-3813 (2000).
34) Ayache A., L´evy V´ehel J. ; The Generalized Multifractional Brownian Motion.
Statistical Inference for Stochastic Processes 3:1-2:7-18 (2000).
35) Ayache A. ; A geometrical solution of a problem on wavelets. Studia Mathematica 139:3:261-273 (2000).
36) Ayache A., L´evy V´ehel J. ; Generalized Multifractional Brownian Motion: defi- nition and preliminary results. Springer, eds Dekind, L´evy V´ehel, Lutton, Tricot 17-32 (1999).
37) Ayache A. ; Construction of non separable dyadic compactly supported wavelet bases forL2(R2) of arbitrarily high regularity. Revista Matematica Iberoamericana15:1:37- 58 (1999).
38) Ayache A. ; Construction de bases d’ondelettes orthonorm´ees de L2(R2) non s´eparables, `a support compact et de r´egularit´e arbitrairememt grande. Comptes Rendus de l’Acad´emie des Sciences de Paris 325:I:17-20, (1997).
LIST OF PUBLICATIONS IN BUSINESS SCIENCES
I) Ayache A., Calciu M., Frandon M., Salerno F. ; Stochastic approach to customer Equity and Lifetime Value calculations with applications to customer retention models and some extensions. EMAC Athens 35-th Conference(2006).
II) Ayache A., Calciu M., Frandon M., Salerno F. ; Calculs de la valeur du client `a l’aide d’une nouvelle approche stochastique et des fonctions g´en´eratrices. 22-`eme Congr`es de l’AFM, Nantes (2006).
III) Ayache A., Calciu M., Frandon M., Salerno F. ; Analytic decision support to find optimal balance between customer acquisition and retention spending. 23-`eme Congr`es de l’AFM, Aix les Bains (2007).
IV) Ayache A., Calciu M., Salerno F. ; Lifetime value calculations in continuous time buying contexts using generating functions and Laplace transforms for customer retention models. 26-`eme Congr`es de l’AFM, Le Mans Angers (2010).
SUPERVISION OF RESEARCH ACTIVITIES
- From September 2007 to November 2011, I was the PhD supervisor of Peng Qidi, whose PhD concerns Statistical inference for hidden multifractional pro- cesses in a setting of stochastic volatility models.
- Since September 2008, I am the PhD supervisor of Hamonier Julien, whose PhD concerns the study of some Stable Multifractional processes by using wavelet methods.
- I have already been the supervisor of five theses in the master 2 Degree of research in Applied Mathematics
PARTICIPATION TO PhD/HABILITATION COMMITTEES
- Member of the committee of Kaim Michael’s PhD “Propri´et´es des lois des fonctionnelles d´efinies sur des processus empiriques : conditions d’absolu continuit´e” de- fended in the “Universit´e Lille 1” on 28 September 2005.
- Referee on Li Xiaolong’s PhD “Etude du processus de Mumford” defended in the “Ecole Normale Sup´erieure de Cachan” on 3 March 2006.
- Referee on Barri`ere Olivier’s PhD “Synth`ese et estimation de Mouvements Browniens Multifractionnaires monodimensionnels et bidimensionnels. Etude de proces- sus `a r´egularit´e prescrite” defended in the “´Ecole Centrale de Nantes” on 28 November 2007.
-Referee and president of the committee of Echelard Antoine’s PhD“Anal- yse 2-microlocale et application au d´ebruitage” defended in the “´Ecole Centrale de Nantes”
on 28 November 2007.
- Referee on Schack Helga’s PhD “An optimal wavelet series expansion of the Riemann-Liouville process” defended in “Friedrich-Schiller-Universit¨at Jena” in Germany on May 2008.
- Referee on Baraka Driss’s PhD “Propri´et´es fines des trajectoires du mouve- ment Brownien fractionnaire” defended in “´Ecole Polytechnique F´ed´erale de Lausanne”
in Switzerland on December 2008.
- President of the committee of Renaud Lopes’s PhD “Analyse fractale et multifractale en imagerie m´edicale : outils, validations et applications” defended in the
“Universit´e Lille 1” on 14 October 2009.
- Member of the committee of Bibi Hatem’s PhD “Construction de bases d’ondelettes de L2([0,1]) et estimation du param`etre de Hurst par la m´ethode des on- delettes” defended in the “Universit´e Paris 1” on 4 November 2011.
-Member of the committee of Peng Qidi’s PhD “Inf´erence statistique pour des processus multifractionnaires cach´es dans un cadre de mod`eles `a volatilit´e stochastique”
defended in the “Universit´e Paris 1” on 4 November 2011.
- Member of the committee of Mate¨ı Basarab’s Habilitation “Parcimonie et diff´erents probl`emes dans le traitement d?images” defended in the “Universit´e Paris 13”
on 7 December 2011.
MAIN TEACHING ACTIVITIES
- I teach ”Probability and Statistics” at all levels.
- During four years (from 2005 to 2008), I gave a course ”on Functional Analysis” in the master 2 Degree of research in Applied Mathematics.
- Since two years, I give a course ”on Stochastic Processes” in the master 2 Degree of research in Applied Mathematics.
- In December 2009, I gave an introductory course ”on Wavelets and Fractional Pro- cesses” at National Taiwan Univerisity in Taiwan.
- In September 2010, I gave an introductory course ”on Fractional and Multifractional Processes” at Wuhan University in China.
- In October 2010, I gave an introductory course ”on Fractional and Multifractional Processes” at the Faculty of Sciences of Monastir in Tunisia.
- In January 2011, I gave an introductory course ”on Wavelets and Fractional Pro- cesses” at the Faculty of Sciences of Monastir in Tunisia.
OTHER ACTIVITIES
- Since August 2012, I am an editor of the Journal of Analysis (http://www.hindawi.com/journals/analysis/editors/).
- Since January 2010, I am an editor of the International Journal of Mathe- maticas and Statistics (http://www.ceser.res.in/ijms.html).
- Since the beginning of January 2012, I am responsible of the seminar “Probabil- ity and Statistics” of the Mathematical research unit “Paul Painlev´e”.
- I am a member of the “ANR AMATIS”
(http://wiki-math.univ-mlv.fr/amatis/doku.php?id=index).
- I am a member of the “GDR Analyse Multifractale”
(http://wiki-math.univ-mlv.fr/gdr3475-am/).
- I was a member of the scientific committee of the Mathematical research unit
“Paul Painlev´e” from the beginning of January 2006 to the end of December 2009.
- In 2009 and 2011, I was a member of recruiting committees (for recruiting professors and assistant professors) at the University Lille 1.
- In 2009 and 2010, I was a member of recruiting committees (for recruiting assistant professors) at the University Paris 12.
- In 2007 and 2008, I was a member of the Specialist Commission in Business Science (for recruiting professors, assistant professors and ATER) at the University of Lille 1. in 2007 and 2008.
- In 2003 and 2004, I was a member of the Specialist Commission in Mathe- matics (for recruiting assistant professors and ATER) at the University of Angers.
- The Colloquium of the Mathematical research unit “Paul Painlev´e” was under my responsability during the academic year 2005-2006.
- I have beenrefereeon about 65 articles submitted to international journals in math- ematics and related fields.
- From 09/1/2003 to 08/31/2004, I was the administrative responsible for the preprints of the research unit CMLA.
- I was one of the four organizers of theinternational congress “Meeting on self- similarity and related fields”which took place in Le Touquet at the beginning of June 2011.
- I was one of the six organizers of theWorkshop “Filtering, MCMC, ABC”which
took place in Lille at the end of March 2011 (http://emmanuel.duflos.ec-lille.fr/WorkshopFP.html).
- I was one of the seven organizers of the international congress “Les journ´ees de Probabilit´es 2008” (The days of Probability 2008)which took place in Lille at
the beginning of September 2008 (http://math.univ-lille1.fr/heinrich/proba2008/).
- I was one of the four organizers of the international congress “Stochastic Processes and Random Fractals” which took place in Lille at the end of March 2006 (http://math.univ-lille1.fr/ sprf/).
- I participated in the organization of the Statistics Seminarof the research unit LSP during the year 2002-2003.
- I participated in the organization of the international congresses “Fractals and Engineering 1999”, “Les journ´ees de Probabilit´es 2003” (The days of Probability 2003) and “Fractals and Engineering 2005”.
INVITATIONS BY UNIVERSITIES OUTSIDE OF FRANCE
• For a period of 6 weeks (from December 1999 to January 2000) by Professor W.M.
Lawton at National University of Singapore.
• For a period of one week in January 2003 by Professor F. Spizzichino atUniversit`a La Sapienza (Roma, Italy).
• For a period of 4 weeks (July and August 2003) by Professor Y. Xiao atMichigan State University, (East Lansing, USA).
• Invited speaker at the Second International Conference on Computational Harmonic Analysis which took place in May 2004 at Vanderbilt University, (Nashville, USA).
• Invited speaker at theInternational Conference “Small Deviation Probabil- ities and Related Topics”which took place in the middle of September 2005 at Steklov Institut of Mathematics, St. Petersburg (Russia).
• For a period of 2 weeks (in December 2009) by Professor N.-R. Shieh at National Taiwan University.
• Invited speaker at the Stochastic Analysis Seminar of the University of Ox- fordin England (February 2010).
• For a period of 1 month (September 2010) by Professor Y. Hu at Wuhan Uni- veristy in China.
• I have been invited by Professor S. Bianchi at University of Cassino in Italyto conduct a two days seminar (December 10).
• For a period of 1 week (January 2011) at Faculty of Sciences of Monastir in Tunisia.
• For a period of 5 days (April 2012) by Professor A. Aldroubi at Vanderbilt Uni- versity, (Nashville, USA).
• For a period of 2 weeks (August and September 2012) by Professor Y. Xiao at Michigan State University, (East Lansing, USA).
• Invited speaker at the Stochastics Seminar of the University of Utah in the USA (September 2012).
INVITATION BY FRENCH UNIVERSITIES AND OTHER FRENCH RESEARCH INSTITUTS
• By the Universities of Amiens, Besan¸con, Clermont-Ferrand 2 (2 times), Dijon, Grenoble 1, Lille 1, Nice, Orl´eans (2 times), Paris 6, Paris 12 (2 times), Paris 13 (2 times), Rennes 1 and Vannes.
• Several times by INRIA (National Research Institut in Computer Science and Au- tomatics).
