Major publications by the team in recent years
  • 1P. Balança, E. Herbin.

    An increment-type set-indexed Markov property, in: Preprint, 2011.
  • 2J. Barral, J. Lévy Véhel.

    Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments, in: Electronic Journal of Probability, 2004, vol. 9, p. 508–543.
  • 3O. Barrière, J. Lévy Véhel.

    Application of the Self Regulating Multifractional Process to cardiac interbeats intervals, in: J. Soc. Fr. Stat., 2009, vol. 150, no 1, p. 54–72.
  • 4F. Chalot, Q. V. Dinh, E. Herbin, L. Martin, M. Ravachol, G. Rogé.

    Estimation of the impact of geometrical uncertainties on aerodynamic coefficients using CFD, in: 10th AIAA Non-Deterministic Approaches, Schaumburg, USA, April 2008.
  • 5F. Chalot, Q. V. Dinh, E. Herbin, L. Martin, M. Ravachol, G. Rogé.

    Estimation of the impact of geometrical uncertainties on aerodynamic coefficients using CFD, in: 10th AIAA Non-Deterministic Approaches Conference, 2008, Schaumburg.
  • 6S. Corlay, J. Lebovits, J. Lévy Véhel.

    Multifractional volatility models, in: preprint, 2011.
  • 7K. Daoudi, J. Lévy Véhel, Y. Meyer.

    Construction of continuous functions with prescribed local regularity, in: Journal of Constructive Approximation, 1998, vol. 014, no 03, p. 349–385.
  • 8Y. Deremaux, J. Négrier, N. Piétremont, E. Herbin, M. Ravachol.

    Environmental MDO and uncertainty hybrid approach applied to a supersonic business jet, in: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization conference, 2008, Victoria.
  • 9A. Echelard, O. Barrière, J. Lévy Véhel.

    Terrain modelling with multifractional Brownian motion and self-regulating processes, in: ICCVG 2010, Warsaw, Poland, Lecture Notes in Computer Science, Springer, 2010, vol. 6374, p. 342-351.

  • 10K. Falconer, R. Le Guèvel, J. Lévy Véhel.

    Localisable moving average stable and multistable processes, in: Stoch. Models, 2009, vol. 25, p. 648–672.
  • 11K. Falconer, J. Lévy Véhel.

    Multifractional, multistable, and other processes with prescribed local form, in: J. Theoret. Probab., 2008, vol. 119, p. 2277–2311, DOI 10.1007/s10959-008-0147-9.
  • 12L. Fermin, J. Lévy Véhel.

    Modeling patient poor compliance in in the multi-IV administration case with Piecewise Deterministic Markov Models, 2011, preprint.
  • 13L. Fermin, J. Lévy Véhel.

    Variability and singularity arising from poor compliance in a pharmacodynamical model II: the multi-oral case, 2011, preprint.
  • 14E. Herbin, B. Arras, G. Barruel.

    From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields, 2010, preprint.
  • 15E. Herbin, P. Balança.

    2-microlocal analysis of martingales and stochastic integrals., in: Preprint available at http://arxiv.org/abs/1107.6016, 2011.
  • 16E. Herbin.

    From n parameter fractional brownian motions to n parameter multifractional brownian motions, in: Rocky Mountain Journal of Mathematics, 2006, vol. 36, no 4, p. 1249–1284.
  • 17E. Herbin, J. Jakubowski, M. Ravachol, Q. V. Dinh.

    Management of uncertainties at the level of global design, in: Symposium "Computational Uncertainties", RTO AVT-147, 2007, Athens.
  • 18E. Herbin, J. Lebovits, J. Lévy Véhel.

    Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motion, in: preprint, 2011.
  • 19E. Herbin, J. Lévy Véhel.

    Stochastic 2-microlocal analysis, in: Stochastic Proc. Appl., 2009, vol. 119, no 7, p. 2277–2311.

  • 20E. Herbin, E. Merzbach.

    A characterization of the set-indexed fractional Brownian motion, in: C. R. Acad. Sci. Paris, 2006, vol. Ser. I 343, p. 767–772.
  • 21E. Herbin, E. Merzbach.

    A set-indexed fractional brownian motion, in: J. of theor. probab., 2006, vol. 19, no 2, p. 337–364.
  • 22E. Herbin, E. Merzbach.

    The multiparameter fractional Brownian motion, in: Math everywhere, Berlin, Springer, Berlin, 2007, p. 93–101.

  • 23E. Herbin, E. Merzbach.

    Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion, in: J. of theor. probab., 2009, vol. 22, no 4, p. 1010–1029.
  • 24E. Herbin, E. Merzbach.

    The set-indexed Lévy process: Stationarity, Markov and sample paths properties, 2010, preprint.
  • 25E. Herbin, A. Richard.

    Hölder regularity for set-indexed processes, in: Submitted, 2011, submitted.
  • 26K. Kolwankar, J. Lévy Véhel.

    A time domain characterization of the fine local regularity of functions, in: J. Fourier Anal. Appl., 2002, vol. 8, no 4, p. 319–334.
  • 27R. Le Guèvel, J. Lévy Véhel.

    A series representation of multistable and other processes, 2008, Submitted to an international journal.
  • 28J. Lebovits, J. Lévy Véhel.

    Stochastic Calculus with respect to multifractional Brownian motion, submitted.

  • 29P.-E. Lévy Véhel, J. Lévy Véhel.

    Variability and singularity arising from poor compliance in a pharmacodynamical model I: the multi-IV case, 2011, preprint.
  • 30J. Lévy Véhel, M. Rams.

    Large Deviation Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments, submitted.

  • 31J. Lévy Véhel, C. Tricot.

    On various multifractal spectra, in: Fractal Geometry and Stochastics III, Progress in Probability, Birkhäuser, ISBN 376437070X, 9783764370701, 2004, vol. 57, p. 23-42, C. Bandt, U. Mosco and M. Zähle (Eds), Birkhäuser Verlag.
  • 32J. Lévy Véhel, R. Vojak.

    Multifractal Analysis of Choquet Capacities: Preliminary Results, in: Advances in Applied Mathematics, January 1998, vol. 20, p. 1–43.
  • 33R. Peltier, J. Lévy Véhel.

    Multifractional Brownian Motion, INRIA, 1995, no 2645.

  • 34M. Ravachol, Y. Deremaux, Q. V. Dinh, E. Herbin.

    Uncertainties at the conceptual stage: Multilevel multidisciplinary design and optimization approach, in: 26th International Congress of the Aeronautical Sciences, 2008, Anchorage.
  • 35F. Roueff, J. Lévy Véhel.

    A Regularization Approach to Fractional Dimension Estimation, in: Fractals'98, 1998, Malta.
  • 36S. Seuret, J. Lévy Véhel.

    A time domain characterization of of 2-microlocal Spaces, in: J. Fourier Anal. Appl., 2003, vol. 9, no 5, p. 472–495.
Publications of the year

Articles in International Peer-Reviewed Journal

  • 37J. Lévy Véhel, F. Mendivil.

    Multifractal and higher dimensional zeta functions, in: Nonlinearity, 2011, vol. 24, no 1, p. 259-276. [ DOI : 10.1088/0951-7715/24/1/013 ]

  • 38J. Lévy Véhel, F. Mendivil.

    Local complex dimensions of a fractal string, in: International Journal of mathematical modelling and numerical optimisation, June 2012.


Internal Reports

  • 39A. Echelard, J. Lévy Véhel.

    Digital Modelling of ECG with multifractional Brownian motion and some of its extensions, Digiteo Anifrac Technical Report, 2011.
  • 40L. Fermin, J. Lévy Véhel.

    Pharmacodynamical analysis of non-compliance, Digiteo Anifrac Technical Report, 2011.

Other Publications

  • 41A. Echelard, J. Lévy Véhel, C. Tricot.

    A Unified Framework for the Study of the 2-microlocal and Large Deviation Multifractal Spectra, 2011, To appear in "Séminaires et Congrès", SMF..

References in notes
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    AIMD, Fairness and Fractal Scaling of TCP Traffic, in: INFOCOM'02, June 2002.
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    Elliptic Gaussian random processes, in: Rev. Mathemàtica Iberoamericana, 1997, vol. 13, no 1, p. 19–90.
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    Second microlocalization and propagation of singularities for semilinear hyperbolic equations, in: Conf. on Hyperbolic Equations and Related Topics, 1984, p. 11–49, Kata/Kyoto,Academic Press, Boston.
  • 45G. Brown, G. Michon, J. Peyrière.

    On the multifractal analysis of measures, in: J. Statist. Phys., 1992, vol. 66, no 3, p. 775–790.
  • 46D. Cacuci.

    Sensitivity and Uncertainty Analysis, Volume 1: Theory., Chapman & Hall/CRC, 2003.
  • 47J. Chiquet, N. Limnios.

    A method to compute the transition function of a piecewise deterministic Markov process with application to reliability, in: Statistics & Probability Letters, 2008, vol. 78, no 12, p. 1397–1403.
  • 48J. Chiquet, N. Limnios, M. Eid.

    Piecewise deterministic Markov processes applied to fatigue crack growth modelling, in: Journal of Statistical Planning and Inference, 2009, vol. 139, no 5, p. 1657–1667.
  • 49M. Davis.

    Markov Models and Optimization, Chapman & Hall, London, 1993.
  • 50 ESReDA.

    Uncertainty in Industrial Practice, a Guide to Quantitative Uncertainty Management, Wiley, 2009.
  • 51K. Falconer.

    The local structure of random processes, in: J. London Math. Soc., 2003, vol. 2, no 67, p. 657–672.
  • 52K. Falconer.

    The multifractal spectrum of statistically self-similar measures, in: J. Theor. Prob., 1994, vol. 7, p. 681–702.
  • 53A. Goldberger, L. A. N. Amaral, J. Hausdorff, P. Ivanov, C. Peng, H. Stanley.

    Fractal dynamics in physiology: Alterations with disease and aging, in: PNAS, 2002, vol. 99, p. 2466–2472.
  • 54G. Ivanoff, E. Merzbach.

    Set-Indexed Martingales, Chapman & Hall/CRC, 2000.
  • 55P. Ivanov, L. A. N. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, Z. Struzik, H. Stanley.

    Multifractality in human heartbeat dynamics, in: Nature, June 1999, vol. 399.
  • 56S. Jaffard.

    Pointwise smoothness, two-microlocalization and wavelet coefficients, in: Publ. Mat., 1991, vol. 35, no 1, p. 155–168.
  • 57H. Kempka.

    2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability, in: Rev. Mat. Complut., 2009, vol. 22, no 1, p. 227–251.
  • 58D. Khoshnevisan.

    Multiparameter Processes: an introduction to random fields, Springer, 2002.
  • 59M. Lapidus, M. van Frankenhuijsen.

    Fractal Geometry and Number Theory (Complex dimensions of fractal strings and zeros of zeta functions), Birkhauser, Boston, 2000.
  • 60J. Li, F. Nekka.

    A Pharmacokinetic Formalism Explicitly Integrating the Patient Drug Compliance, in: J. Pharmacokinet. Pharmacodyn., 2007, vol. 34, no 1, p. 115–139.
  • 61J. Li, F. Nekka.

    A probabilistic approach for the evaluation of pharmacological effect induced by patient irregular drug intake, in: J. Pharmacokinet. Pharmacodyn., 2009, vol. 36, no 3, p. 221–238.
  • 62M. B. Marcus, J. Rosen.

    Markov Processes, Gaussian Processes and Local Times, Cambridge University Press, 2006.
  • 63J. Rosinski.

    Tempering stable processes, in: Stochastic Processes and Their Applications, 2007, vol. 117, no 6, p. 677–707.
  • 64G. Samorodnitsky, M. Taqqu.

    Stable Non-Gaussian Random Processes, Chapman and Hall, 1994.
  • 65S. Stoev, M. Taqqu.

    Stochastic properties of the linear multifractional stable motion, in: Adv. Appl. Probab., 2004, vol. 36, p. 1085–1115.
  • 66B. Vrijens, J. Urquhart.

    New findings about patient adherence to prescribed drug dosing regimens: an introduction to pharmionics, in: Eur. J. Hosp. Pharm. Sci., 2005, vol. 11, no 5, p. 103–106.
  • 67B. Vrijens, J. Urquhart.

    Patient adherence to prescribed antimicrobial drug dosing regimens, in: J. Antimicrob. Chemother., 2005, vol. 55, p. 616–627.