Bibliography
Major publications by the team in recent years
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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.
http://hal. inria. fr/ inria-00538907/ en -
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.
http://arxiv. org/ abs/ math. PR/ 0504551 -
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.
http://dx. doi. org/ 10. 1007/ 978-3-540-44446-6_8 -
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.
http://hal. inria. fr/ inria-00580196/ en -
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.
http://hal. inria. fr/ inria-00633195/ en -
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.
http://hal. inria. fr/ inria-00074045 -
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.
Articles in International Peer-Reviewed Journal
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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 ]
http://hal. inria. fr/ inria-00538956/ en -
38J. Lévy Véhel, F. Mendivil.
Local complex dimensions of a fractal string, in: International Journal of mathematical modelling and numerical optimisation, June 2012.
http://hal. inria. fr/ inria-00614665/ en
Internal Reports
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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
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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..
http://hal. inria. fr/ inria-00612342/ en
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42F. Baccelli, D. Hong.
AIMD, Fairness and Fractal Scaling of TCP Traffic, in: INFOCOM'02, June 2002. -
43A. Benassi, S. Jaffard, D. Roux.
Elliptic Gaussian random processes, in: Rev. Mathemàtica Iberoamericana, 1997, vol. 13, no 1, p. 19–90. -
44J. 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. -
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.