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

    A increment type set-indexed Markov property, 2012.

  • 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.
  • 5K. 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.
  • 6Y. 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.
  • 7A. 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.

  • 8K. Falconer, R. Le Guével, J. Lévy-Véhel.

    Localisable moving average stable and multistable processes, in: Stoch. Models, 2009, vol. 25, p. 648–672.
  • 9K. 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.
  • 10L. Fermin, J. Lévy-Véhel.

    Modeling patient poor compliance in in the multi-IV administration case with Piecewise Deterministic Markov Models, 2011, preprint.
  • 11L. Fermin, J. Lévy-Véhel.

    Variability and singularity arising from poor compliance in a pharmacodynamical model II: the multi-oral case, 2011, preprint.
  • 12E. Herbin, B. Arras, G. Barruel.

    From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields, 2010, preprint.
  • 13E. 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.
  • 14E. 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.
  • 15E. Herbin, J. Lebovits, J. Lévy-Véhel.

    Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motion, in: preprint, 2011.
  • 16E. Herbin, J. Lévy-Véhel.

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

  • 17E. 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.
  • 18E. Herbin, E. Merzbach.

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

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

  • 20E. 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.
  • 21E. Herbin, E. Merzbach.

    The set-indexed Lévy process: Stationarity, Markov and sample paths properties, 2010, preprint.
  • 22E. Herbin, A. Richard.

    Hölder regularity for set-indexed processes, in: Submitted, 2011, submitted.
  • 23K. 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.
  • 24J. Lebovits, J. Lévy-Véhel.

    Stochastic Calculus with respect to multifractional Brownian motion, submitted.

  • 25J. Lévy-Véhel, M. Rams.

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

  • 26J. 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.
  • 27J. Lévy-Véhel, R. Vojak.

    Multifractal Analysis of Choquet Capacities: Preliminary Results, in: Advances in Applied Mathematics, January 1998, vol. 20, p. 1–43.
  • 28R. Peltier, J. Lévy-Véhel.

    Multifractional Brownian Motion, Inria, 1995, no 2645.

  • 29M. 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.
  • 30F. Roueff, J. Lévy-Véhel.

    A Regularization Approach to Fractional Dimension Estimation, in: Fractals'98, 1998, Malta.
  • 31S. 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 Journals

  • 32P. Balança, E. Herbin.

    A set-indexed Ornstein-Uhlenbeck process, in: Electronic Communications in Probability, 2012, vol. 17, no 39, p. 1-14, 13 pages. [ DOI : 10.1214/ECP.v17-1903 ]

  • 33P. Balança, E. Herbin.

    2-microlocal analysis of martingales and stochastic integrals, in: Stochastic Processes and their Applications, 2012, vol. 122, p. 2346-2382, 40 pages, 3 figures. [ DOI : 10.1016/j.spa.2012.03.011 ]

  • 34S. Corlay, J. Lebovits, J. Lévy-Véhel.

    Multifractional Stochastic volatility models, in: Mathematical Finance, September 2012, Accepted for Publication.

  • 35R. Le Guével, J. Lévy-Véhel.

    A Ferguson - Klass - LePage series representation of multistable multifractional processes and related processes, in: Bernoulli, 2012, vol. 18, no 4, p. 1099-1127. [ DOI : 10.3150/11-BEJ372 ]

  • 36J. Lévy-Véhel, F. Mendivil.

    Local complex dimensions of a fractal string, in: International Journal of mathematical modelling and numerical optimisation, October 2012, vol. 3, no 4.

  • 37L. Trujillo, P. Legrand, G. Olague, J. Lévy-Véhel.

    Evolving Estimators of the Pointwise Holder Exponent with Genetic Programming, in: Information Sciences, 2012, vol. 209, p. 61-79, Submitted. [ DOI : 10.1016/j.ins.2012.04.043 ]


International Conferences with Proceedings

  • 38A. Echelard, J. Lévy-Véhel.

    Self-regulating processes-based modelling for arrhythmia characterization, in: Imaging and Signal Processing in Health Care and Technology, Baltimore, United States, May 2012.


Conferences without Proceedings

  • 40A. Echelard, J. Lévy-Véhel, C. Tricot.

    A Unified Framework for the Study of the 2-microlocal and Large Deviation Multifractal Spectra, in: Self similar processes and their applications, Angers, France, SMF, 2012, p. 13-44.


Other Publications

  • 41B. Arras.

    On a class of self-similar processes with stationary increments in higher order Wiener chaoses, 2012, 21 pages.

  • 42O. Barrière, A. Echelard, J. Lévy-Véhel.

    Self-Regulating Processes, To appear in the Electronic Journal of Probability.

  • 43R. Le Guével, J. Lévy-Véhel, L. Liu.

    On two multistable extensions of stable Lévy motion and their semimartingale representation.

  • 44P.-E. Lévy-Véhel, J. Lévy-Véhel.

    Variability and singularity arising from poor compliance in a pharmacokinetic model I: the multi-IV case, To appear in Journal of Pharmacokinetics and Pharmacodynamics..

  • 45J. Lévy-Véhel, F. Mendivil.

    Christiane's Hair, To appear in the American Mathematical Monthly.

References in notes
  • 46A. Ayache, Y. Xiao.

    Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets, in: J. Fourier Anal. Appl., 2005, vol. 11, no 4, p. 407–439.

  • 47F. Baccelli, D. Hong.

    AIMD, Fairness and Fractal Scaling of TCP Traffic, in: INFOCOM'02, June 2002.
  • 48R. M. Balan, G. Ivanoff.

    A Markov property for set-indexed processes, in: J. Theoret. Probab., 2002, vol. 15, no 3, p. 553–588.

  • 49A. Benassi, S. Jaffard, D. Roux.

    Elliptic Gaussian random processes, in: Rev. Mathemàtica Iberoamericana, 1997, vol. 13, no 1, p. 19–90.
  • 50J. Bony.

    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.
  • 51G. Brown, G. Michon, J. Peyrière.

    On the multifractal analysis of measures, in: J. Statist. Phys., 1992, vol. 66, no 3, p. 775–790.
  • 52D. Cacuci.

    Sensitivity and Uncertainty Analysis, Volume 1: Theory., Chapman & Hall/CRC, 2003.
  • 53R. Cairoli.

    Une classe de processus de Markov, in: C. R. Acad. Sci. Paris Sér. A-B, 1971, vol. 273, p. A1071–A1074.
  • 54A. Carbery, J. Wright.

    Distributional and L q norm inequalities for polynomials over convex bodies in R n , in: Math. Res. Lett., 2001, vol. 8, no 3, p. 233–248.
  • 55F. Comte, E. Renault.

    Long memory in continuous-time stochastic volatility models, in: Mathematical Finance, 1998, vol. 8, no 4, p. 291–323.

  • 56M. Davis.

    Markov Models and Optimization, Chapman & Hall, London, 1993.
  • 57J. Doob.

    Stochastic Processes, Wiley, 1953.
  • 58 ESReDA.

    Uncertainty in Industrial Practice, a Guide to Quantitative Uncertainty Management, Wiley, 2009.
  • 59K. Falconer.

    The local structure of random processes, in: J. London Math. Soc., 2003, vol. 2, no 67, p. 657–672.
  • 60K. Falconer.

    The multifractal spectrum of statistically self-similar measures, in: J. Theor. Prob., 1994, vol. 7, p. 681–702.
  • 61A. 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.
  • 62G. Ivanoff, E. Merzbach.

    Set-Indexed Martingales, Chapman & Hall/CRC, 2000.
  • 63P. 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.
  • 64S. Jaffard.

    Pointwise smoothness, two-microlocalization and wavelet coefficients, in: Publ. Mat., 1991, vol. 35, no 1, p. 155–168.
  • 65S. Jaffard.

    The multifractal nature of Lévy processes, in: Probab. Theory Related Fields, 1999, vol. 114, no 2, p. 207–227.

  • 66H. Kempka.

    2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability, in: Rev. Mat. Complut., 2009, vol. 22, no 1, p. 227–251.
  • 67D. Khoshnevisan.

    Multiparameter Processes: an introduction to random fields, Springer, 2002.
  • 68D. Khoshnevisan.

    Multiparameter processes: An Introduction to Random Fields, Springer Monographs in Mathematics, Springer-Verlag, New York, 2002, xx+584 p.
  • 69J. Lamperti.

    Semi-stable stochastic processes, in: Trans. Am. Math. Soc., 1962, vol. 104, p. 62-78.
  • 70J. Li, F. Nekka.

    A Pharmacokinetic Formalism Explicitly Integrating the Patient Drug Compliance, in: J. Pharmacokinet. Pharmacodyn., 2007, vol. 34, no 1, p. 115–139.
  • 71J. 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.
  • 72M. B. Marcus, J. Rosen.

    Markov Processes, Gaussian Processes and Local Times, Cambridge University Press, 2006.
  • 73T. Mori, H. Oodaira.

    The law of the iterated logarithm for self-similar processes represented by multiple Wiener integrals, in: Probab. Theory Relat. Fields, 1986, vol. 71, no 3, p. 367–391.

  • 74G. Samorodnitsky, M. Taqqu.

    Stable Non-Gaussian Random Processes, Chapman and Hall, 1994.
  • 75S. Stoev, M. Taqqu.

    Stochastic properties of the linear multifractional stable motion, in: Adv. Appl. Probab., 2004, vol. 36, p. 1085–1115.
  • 76B. 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.
  • 77B. Vrijens, J. Urquhart.

    Patient adherence to prescribed antimicrobial drug dosing regimens, in: J. Antimicrob. Chemother., 2005, vol. 55, p. 616–627.
  • 78Y. Xiao, H. Lin.

    Dimension properties of sample paths of self-similar processes, in: Acta Math. Sinica (N.S.), 1994, vol. 10, no 3, p. 289–300, A Chinese summary appears in Acta Math. Sinica 38 (1995), no. 4, 576.