Updated Curriculum vitae in English
Mathematical fields of research:
Fractal stochastic processes (study of some properties of their trajectories and estimation of their parameters).Wavelets.
Mathematical papers:
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Ayache, A.
Construction de bases d'ondelettes orthonormées de L2(R2) non séparables, à support compact et de régularité arbitrairememt grande.
Comptes Rendus Académie des Sciences de Paris 325, I, 17-20, (1997).
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Ayache, A.
Construction of non separable dyadic compactly supported wavelet bases for L2(R2) of arbitrarily high regularity.
Revista Matematica Iberoamericana 15, 1, 37-58 (1999).
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Ayache, A.
A geometrical solution of a problem on wavelets.
Studia Mathematica (2000).
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Ayache, A.
Some methods for constructing non separable, orthonormal, compactly supported wavelet bases.
Letter to the editor in Applied and Computational Harmonic Analysis 10, 99-111 (2001) .
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Ayache, A.; Lévy Véhel, J.
Generalized Multifractional Brownian Motion: definition and preliminary results.
Springer, eds Dekind, Lévy Véhel, Lutton, Tricot (1999).
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Ayache, A.; Lévy Véhel, J.
The Generalized Multifractional Brownian Motion.
Statistical Inference for Stochastic Processes 3, 1-2, 7-18 (2000).
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Ayache, A.; Cohen, S.; Lévy Véhel, J.
The covariance structure of multifractional Brownian motion.
ICASSP (2000).
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Ayache, A.; Lévy Véhel, J.
Processus à régularité locale prescrite.
Comptes Rendus Académie des Sciences de Paris 333, I, 233-238, (2001).
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Ayache, A.
Du mouvement brownien fractionnaire au mouvement brownien multifractionnaire.
Technique et science informatiques. Volume 20 - n° 9, 1133-1152 (2001).
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Ayache, A.
The Generalized Multifractional Field: a nice tool for the study of the Generalized Multifractional Brownian Motion.
Jour. Fourier Anal. Appl. Volume 8, Issue 6 (2002).
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Ayache, A.; Léger, S.; Pontier, M.
Drap Brownien Fractionnaire.
Potential Analysis 17: 31-43, (2002).
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Ayache, A.; Léger, S.; Pontier, M.
Les ondelettes à la conquete du Drap Brownien Fractionnaire.
Comptes Rendus Académie des Sciences de Paris 335, I, 1063-1068, (2002).
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Ayache, A.; Roueff F.,
A Fourier formulation of the Frostman criterion for random graphs and its application to wavelet series.
Letter to the editor in Applied and Computational Harmonic Analysis 14, 75-82 (2003).
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Ayache, A. ; Taqqu M.S.
Rate optimality of wavelet series approximations of fractional Brownian Motion.
Jour. Fourier Anal. Appl. Volume 9, Issue 5 (2003)
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Ayache, A.
Hausdorff dimension of the graph of the Fractional Brownian Sheet.
Revista Matematica Iberoamericana 2, 20, 395-412 (2004).
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Ayache, A. ; Lévy Véhel, J.
Identification of the pointwise Holder exponent of Generalized Multifractional Brownian Motion.
Stochastic Processes and their Applications 111, 119-156 (2004).
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Ayache, A. ; Benassi, A. ; Cohen, S. ; Lévy Véhel, J.
Regularity and identification of Generalized Multifractional Gaussian Process.
Séminaire de Probabilités (2005).
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Ayache, A. ; Xiao, Y.
Asymptotic Growth Properties and Hausdorff dimensions of Fractional Brownian Sheets.
Jour. Fourier Anal. Appl. Volume 11, Issue 4, 407-439 (2005).
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Ayache, A. ; Taqqu, M.S.
Multifractional Processes with Random Exponent.
Publicacions Matemàtiques 49, 459-486 (2005).
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Ayache, A. ; Heinrich, P. ; Marsalle, L. ; Suquet, Ch.
Holderian random functions.
Fractals in Engineering. New Trends in Theory and Applications. Springer-Verlag eds, Lévy Véhel, Lutton (2005).
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Ayache, A. ; Jaffard, S. ; Taqqu, M.S.
Wavelet construction of generalized multifractional processes.
Revista Matematica Iberoamericana 23, 1, 327-370 (2007).
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Ayache, A. ; Bonami, A. ; Estrade, A.
Identification and wavelet decomposition of anisotropic Gaussian fields.
To appear in Proceedings of 5th ISAAC Congress, 25-30 July 2005, University of Catania, World Scientific.
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Ayache, A. ; Bertrand, P. ; Lévy Véhel, J.
A central limit theorem for the quadratic variations of the step fractional Brownian motion.
Statistical Inference for Stochastic Processes 10, 1-27 (2007).
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Ayache, A. ; Linde, W.
Approximation of Gaussian Fields: General results and optimal wavelet representation of the Lévy Fractional Motion.
Journal of Theoretical Probability 21, 69-96 (2008).
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Ayache, A. ; Tzvetkov, N.
L^p properties for Gaussian random series.
Transactions of the American Mathematical Society 360, 4425-4439 (2008).
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Ayache, A. ; Dongsheng, W. ; Xiao, Y.
Joint continuity of the Local times of Fractional Brownian Sheets.
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 44, 4, 727-748 (2008).
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Ayache, A. ; Roueff, F. ; Xiao, Y.
Local and asymptotic properties of Linear Fractional Stable Sheets.
Comptes Rendus de l'Académie des Sciences de Paris 344, I, 389-394 (2007).
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Ayache, A. ; Roueff, F. ; Xiao, Y.
Joint continuity of the local times of Linear Fractional Stable Sheets.
Comptes Rendus de l'Académie des Sciences de Paris 344, I, 635-640 (2007).
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Ayache, A. ; Roueff, F. ; Xiao, Y.
Linear Fractional Stable Sheets: Wavelet expansion and sample properties.
To appear in Stochastic Processes and their Applications.
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Ayache, A. ; Jaffard, S.
Hölder exponents of arbitray funtions.
To appear in Revista Matematica Iberoamericana.
Other papers:
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Ayache, A.; Calciu, M.; Fradon, M. ; Salerno, F.
Stochastic approach to customer Equity and Lifetime Value calculations with applications to customer retention models and some extentions.
Athens, 35th Annual Conference of the European Marketing Academy, 23-26 May (2006).
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Ayache, A.; Calciu, M.; Fradon, M. ; Salerno, F.
Calcul de la valeur du client à l'aide d'une nouvelle approche stochastique et des fonctions génératrices.
22ème Congrès international de l'Association Française de Marketing, Nantes 11-12 Mai (2006).
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Ayache, A.; Calciu, M.; Fradon, M. ; Salerno, F.
Analytic decision support to find optimal balance between customer acquisition and retention spending.
23ème Congrès international de l'Association Française de Marketing, Aix les Bains, 30 Mai - 1 Juin (2007).
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