Bibliography

Major publications by the team in recent years

1P. Balança.

A increment type set-indexed Markov property, 2012.

http://arxiv.org/abs/1207.6568
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, n^o 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, n^o 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.

http://hal.inria.fr/inria-00538907/en
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, n^o 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, n^o 7, p. 2277–2311.

http://arxiv.org/abs/math.PR/0504551
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, n^o 2, p. 337–364.
19E. 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
20E. Herbin, E. Merzbach.

Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion, in: J. of theor. probab., 2009, vol. 22, n^o 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, n^o 4, p. 319–334.
24J. Lebovits, J. Lévy-Véhel.

Stochastic Calculus with respect to multifractional Brownian motion, submitted.

http://hal.inria.fr/inria-00580196/en
25J. 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
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, n^o 2645.

http://hal.inria.fr/inria-00074045
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, n^o 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, n^o 39, p. 1-14, 13 pages. [ DOI : 10.1214/ECP.v17-1903 ]

http://hal.inria.fr/hal-00734421
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 ]

http://hal.inria.fr/hal-00734418
34S. Corlay, J. Lebovits, J. Lévy-Véhel.

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

http://hal.inria.fr/hal-00653150
35R. Le Guével, J. Lévy-Véhel.

A Ferguson - Klass - LePage series representation of multistable multifractional processes and related processes, in: Bernoulli, 2012, vol. 18, n^o 4, p. 1099-1127. [ DOI : 10.3150/11-BEJ372 ]

http://hal.inria.fr/inria-00538985
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, n^o 4.

http://hal.inria.fr/inria-00614665
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 ]

http://hal.inria.fr/hal-00643387

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.

http://hal.inria.fr/hal-00670064

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.

http://hal.inria.fr/inria-00612342

Other Publications

41B. Arras.

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

http://hal.inria.fr/hal-00759165
42O. Barrière, A. Echelard, J. Lévy-Véhel.

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

http://hal.inria.fr/hal-00749742
43R. Le Guével, J. Lévy-Véhel, L. Liu.

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

http://hal.inria.fr/hal-00730680
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..

http://hal.inria.fr/hal-00752114
45J. Lévy-Véhel, F. Mendivil.

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

http://hal.inria.fr/hal-00744268

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62G. Ivanoff, E. Merzbach.

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