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Journal papers and preprints
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Abry, P., Didier, G., Orejola, O. and Wendt,
H. (2024), 'On the empirical spectral
distribution of large wavelet random matrices based on
mixed-Gaussian fractional measurements in moderately
high dimensions'. Under
review,
pp.1-52.
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Lucas,
C.-G., Didier, G., Wendt, H. and Abry,
P. (2024), 'Multivariate selfsimilarity:
Multiscale eigen-structures for selfsimilarity
parameter estimation'. To appear in IEEE
Transactions on Signal Processing, pp.1-11.
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Didier, G., Glatt-Holtz, N.E.,
Holbrook, A.J., Magee, A.F., Suchard,
M.A. (2024), 'On
the surprising effectiveness of a simple
matrix exponential derivative approximation,
with application to global SARS-CoV-2'. Proceedings of the
National Academy of Sciences of the U.S.A., 121(3),
e231898912.
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Abry, P., Boniece, B.C., Didier, G. and Wendt, H. (2021), 'On
high-dimensional wavelet eigenanalysis'. Under review, pp.1-56.
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Abry, P., Boniece, B.C., Didier, G. and Wendt, H. (2023), 'Wavelet
eigenvalue regression in high dimensions'.
Statistical Inference for Stochastic
Processes 26(1),
1-32.
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Didier, G. and Nguyen, H. (2022), 'The generalized Langevin
equation in harmonic potentials: anomalous
diffusion and equipartition of energy'. Communications in Mathematical
Physics, 393(2), pp.909¨C954.
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Boniece, B.C. and Didier, G. (2022), 'On operator fractional L¨¦vy
motion: integral representations and time
reversibility'. Advances in Applied
Probability, 54(2),
pp.493¨C535.
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Zhang,
K. and Didier, G. (2021), 'Asymptotic theory for the
detection of mixing in anomalous diffusion'. Journal of Mathematical Physics 62,
063301.
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Boniece, B.C., Didier, G. and Sabzikar, F. (2021), 'Tempered fractional Brownian
motion: wavelet estimation, modeling and testing'. Applied and Computational
Harmonic Analysis, 51, March, pp.461-509.
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Didier, G., Kanamori,
S. and Sabzikar,
F. (2021), 'On multivariate fractional
random fields: tempering and operator-stable laws'. Journal
of Mathematical Analysis and Applications, 495(1), 124659.
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Didier,
G. and Nguyen,
H. (2020), 'Asymptotic
analysis of the mean squared displacement under
fractional memory kernels'. SIAM
Journal on Mathematical Analysis, 52(4), pp.3818-3842.
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Boniece, B.C., Didier, G. and Sabzikar, F. (2020), 'On fractional L¨¦vy processes:
tempering, sample path properties and stochastic
integration'. Journal of Statistical Physics,
178(4), pp.954-985.
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Abry, P.,
Wendt, H.,
Jaffard,
S. and Didier, G. (2019), 'Multivariate
scale-free temporal dynamics: From spectral (Fourier) to
fractal (wavelet) analysis'. Comptes Rendus [de l'Acad¨¦mie des Sciences]
Physique, 20(5), July-August,
pp.489-501.
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Abry, P., Didier, G. and Li, H. (2019), 'Two-step
wavelet-based estimation for Gaussian mixed fractional
processes'. Statistical Inference for
Stochastic Processes, 22(2), July,
pp.157-185.
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Zhang, K., Crizer, K. P. R.,
Schoenfisch,
M. H., Hill,
D. B. and Didier, G. (2018), 'Fluid
heterogeneity detection based on the asymptotic
distribution of the time-averaged mean squared
displacement in single particle tracking experiments'. Journal of Physics A:
Mathematical and Theoretical, 51 445601.
[remark: paper selected for the Journal of
Physics A Highlights of 2018 collection]
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Abry, P. and Didier, G. (2018), 'Wavelet
eigenvalue regression for n-variate operator fractional Brownian
motion'. Journal of Multivariate
Analysis, 168,
November, pp. 75-104.
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Didier, G., Meerschaert, M.
M. and Pipiras,
V. (2018), 'Domain and range symmetries of
operator fractional Brownian fields'. Stochastic Processes and their Applications, 128(1), pp. 39-78.
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Abry, P. and Didier, G. (2018), 'Wavelet
estimation for operator fractional Brownian motion', Bernoulli, 24(2), pp. 895-928.
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Wendt, H.,
Didier, G., Combrexelle, S. and Abry, P.,
(2017), 'Multivariate
Hadamard self-similarity: testing fractal connectivity', Physica D: Nonlinear Phenomena, 356-357, pp. 1-36.
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Didier, G. and
Zhang., K. (2017), 'The asymptotic distribution of the
pathwise mean squared displacement in single particle
tracking experiments', Journal
of Time Series Analysis, 38(3), May, pp. 395-416.
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Didier, G.,
Meerschaert, M. M. and Pipiras, V. (2017), 'Exponents of operator self-similar
random fields', Journal of Mathematical Analysis and
Applications, 448(2), pp. 1450¨C1466.
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Frecon, J., Didier, G., Pustelnik,
N. and Abry, P. (2016), 'Non-linear wavelet regression and
branch & bound optimization for the full
identification of bivariate operator fractional Brownian
motion', IEEE Transactions on
Signal Processing, 64(15), pp. 4040-4049.
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Baek, C.,
Didier, G. and Pipiras, V. (2014), 'On integral
representations of operator fractional Brownian fields',
Statistics and Probability
Letters, 92, 190-198.
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Didier, G. and Fricks, J. (2014), 'On
the
wavelet-based simulation of anomalous diffusion', Journal
of Statistical Computation and Simulation, 84(4), pp. 697-723.
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Didier, G., Jaffard, S. and Pipiras,
V. (2013), 'On
the vaguelet and Riesz properties of L2-unbounded
transformation of orthogonal wavelet bases', Journal
of Approximation Theory, vol. 176, December, pp.
94-117.
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Didier, G., McKinley, S.A., Hill,
D.B. and Fricks, J. (2012), 'Statistical
challenges in microrheology', Journal
of Time Series Analysis, 33(5), September,
pp. 724-743.
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Didier, G. and Pipiras, V. (2012), 'Exponents,
symmetry
groups
and
classification of operator fractional Brownian motions', Journal
of Theoretical Probability, 25(2), pp. 353¨C395.
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Didier, G. and Pipiras, V.
(2011), 'Integral
representations and properties of operator fractional
Brownian motions', Bernoulli 17(1), pp. 1-33.
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Didier, G. and Pipiras, V.
(2010), 'Adaptive
wavelet
decompositions
of stationary time series', Journal of Time Series
Analysis, 31(3),
May, pp. 182-209.
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Belloni,
A. and Didier, G. (2008), 'On
the Behrens-Fisher problem: a globally convergent
algorithm and a finite-sample study of the Wald, LR and LM
Tests', Annals
of Statistics, 36(5),
pp. 2377-2408.
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Didier,
G. and Pipiras, V. (2008), 'Gaussian
stationary processes: discrete approximations, adaptive
wavelet decompositions and their convergence',
Journal of
Fourier Analysis and Applications, 14(2), April,
pp.203-234.
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Conference
papers
(peer-reviewed) and preprints
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Lucas,
C.-G., Abry,
P., Wendt, H. and Didier, G. (2023), 'Epileptic seizure prediction
from eigen-wavelet multivariate self-similarity
analysis of multi-channel EEG signals'.
31st
European Signal Processing Conference (EUSIPCO), Helsinki, Finland, pp.1-5.
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Lucas,
C.-G., Abry, P., Wendt, H., Didier, G. and Orejola, O. (2023), 'Bootstrap based test for the
unimodality of estimated Hurst exponents: performance
assessment in a high-dimensional analysis setting'.
XXIX¨¨me Colloque Francophone de Traitement du Signal
et des Images (GRETSI), Grenoble, France, pp.1-5.
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Lucas,
C.-G., Wendt, H., Abry, P., and Didier, G. (2022), 'Multivariate time-scale
bootstrap for testing the equality of selfsimilarity
parameters'. XXVIII¨¨me
Colloque Francophone de Traitement du Signal et des
Images (GRETSI), Nancy, France, pp.1-5.
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Orejola,
O., Didier, G., Wendt, H. and Abry, P. (2022), 'Hurst multimodality
detection based on large wavelet random matrices'. 30th European Signal
Processing Conference (EUSIPCO), Belgrade, Serbia, pp.1-5.
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Lucas,
C.-G., Abry, P., Wendt, H. and Didier, G. (2022), 'Drowsiness detection from
polysomnographic data using multivariate
selfsimilarity and eigen-wavelet analysis'. 44th
Annual International Conference of the IEEE
Engineering in Medicine & Biology Society (EMBC
2022), Glasgow, U.K., pp.1-5.
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Lucas,
C.-G., Abry, P., Wendt, H. and Didier, G. (2022), 'Counting the number of
different scaling exponents in multivariate scale-free
dynamics: clustering by bootstrap in the wavelet
domain'.
IEEE International Conference on Acoustics,
Speech and Signal Processing (ICASSP), Singapore, pp.5513-5517.
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Lucas,
C.-G., Abry, P., Wendt, H. and Didier, G. (2021), 'Bootstrap for testing the
equality of selfsimilarity exponents across
multivariate time series'. 29th European Signal
Processing Conference (EUSIPCO), Dublin, Ireland, pp.1-5.
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Catrambone,
V., Abry, P., Valenza, G., Wendt, H., Didier, G. and
Barbieri, R. (2020), 'Multiscale eigen analysis on
EEG and heartbeat dynamics: a pilot study'. 11th
Conference of the European Study Group on
Cardiovascular Oscillations (ESGCO), Pisa, Italy, pp.1-2.
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Boniece,
B.C., Wendt,
H., Didier, G. and Abry, P. (2019), 'Wavelet-based detection and
estimation of fractional L¨¦vy signals in high
dimensions'. 8th
IEEE International Workshop on Computational Advances
in Multi-Sensor Adaptive Processing (CAMSAP), Le Gosier, Guadeloupe, pp.1-5.
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Boniece,
B.C., Didier,
G., Wendt,
H., and Abry,
P. (2019), 'On multivariate non-Gaussian
scale invariance: fractional L¨¦vy processes and
wavelet estimation'. 27th European Signal
Processing Conference (EUSIPCO), A Coruña, Spain, pp.1-5.
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Didier,
G., Wendt,
H. and Abry, P. (2019), 'Detection and estimation of
delays in bivariate self-similarity: bootstrapped
complex wavelet coherence'.
IEEE International Conference on Acoustics,
Speech and Signal Processing (ICASSP),
Brighton, U.K., pp.1-5.
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Wendt, H., Abry, P. and Didier, G. (2019), 'Bootstrap-based bias
reduction for the estimation of the self-similarity
exponents of multivariate time series'. IEEE
International Conference on Acoustics, Speech and
Signal Processing (ICASSP),
Brighton, U.K., pp.1-5.
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Abry, P., Wendt, H. and Didier, G. (2018), 'Detecting and estimating
multivariate self-similar sources in high-dimensional
mixtures',
IEEE Statistical
Signal Processing Workshop, Freiburg,
Germany, pp.1-5.
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Boniece, B.C., Sabzikar, F. and Didier, G. (2018), 'Tempered fractional Brownian
motion: wavelet estimation and modeling of turbulence
in geophysical flows', IEEE Statistical Signal
Processing Workshop, Freiburg, Germany, pp.1-5.
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Wendt, H., Abry, P. and Didier, G. (2018), 'Wavelet domain bootstrap for
testing the equality of bivariate self-similarity
exponents', IEEE Statistical Signal Processing
Workshop, Freiburg, Germany,
pp.1-5.
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Combrexelle, S., Wendt, H., Didier, G. and Abry,
P. (2017), 'Multivariate scale-free
dynamics: testing fractal connectivity',
IEEE International Conference on Acoustics, Speech and
Signal Processing (ICASSP), New
Orleans, USA, pp.1-5.
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Frecon, J., Fontugne, R., Didier, G., Pustelnik,
N., Fukuda, K. and Abry, P. (2016), 'Non-linear regression for
bivariate self-similarity identification -- application
to anomaly detection in Internet traffic based on a
joint scaling analysis of packet and byte counts',
IEEE
International Conference on Acoustics, Speech and Signal
Processing (ICASSP), Shanghai, China, pp.1-5.
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Didier, G., Helgason, H. and Abry, P. (2015), 'Demixing multivariate-operator
self-similar processes', IEEE International Conference on
Acoustics, Speech and Signal Processing (ICASSP),
Brisbane, Australia, pp.1-5.
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