Research
 



Research Interests


  • random processes and fields (fractional/self-similar, anomalous diffusion)
  • wavelets and applied harmonic analysis
  • high-dimensional probability, random matrices and (time series) applications
  • mathematical biology (nanobiophysics) and signal processing



Journal papers and preprints




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.



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.



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.



Abry, P., Boniece, B.C., Didier, G. and Wendt, H. (2021), 'On high-dimensional wavelet eigenanalysis'. Under review, pp.1-56.



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.



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.



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.



Zhang, K. and Didier, G. (2021), 'Asymptotic theory for the detection of mixing in anomalous diffusion'. Journal of Mathematical Physics 62, 063301.



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.



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.



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.



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.



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.



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.



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] 




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.



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.



Abry, P. and Didier, G. (2018), 'Wavelet estimation for operator fractional Brownian motion', Bernoulli, 24(2), pp. 895-928.



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.



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.



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.



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.



Baek, C., Didier, G. and Pipiras, V. (2014), 'On integral representations of operator fractional Brownian fields', Statistics and Probability Letters, 92, 190-198.



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.



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.



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.



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.




Didier, G. and Pipiras, V. (2011), 'Integral representations and properties of operator fractional Brownian motions', Bernoulli 17(1), pp. 1-33.



Didier, G. and Pipiras, V. (2010), 'Adaptive wavelet decompositions of stationary time series', Journal of Time Series Analysis, 31(3), May, pp. 182-209.



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.



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.






Conference papers (peer-reviewed) and preprints



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.



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.


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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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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