Research
 



Research Interests


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



Journal papers and preprints




Didier, G. and Nguyen, H. (2019), 'Asymptotic analysis of the mean squared displacement under fractional memory kernels'. Under review, pp.1-33.



Boniece, B.C., Didier, G. and Sabzikar, F. (2018), 'On fractional Lvy processes: tempering, sample path properties and stochastic integration'. Under review, pp.1-46.



Boniece, B.C., Didier, G. and Sabzikar, F. (2018), 'Tempered fractional Brownian motion: wavelet estimation, modeling and testing'. Under review, pp.1-48.



Abry, P., Didier, G. and Li, H. (2018), 'Two-step wavelet-based estimation for Gaussian mixed fractional processes'. To appear in Statistical Inference for Stochastic Processes, pp. 1-60.



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. 1450C1466.



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. 353C395.




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



Boniece, B.C., Didier, G., Wendt, H., and Abry, P. (2019), 'On multivariate non-Gaussian scale invariance: fractional Lvy processes and wavelet estimation'. Under review, 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'.  To appear in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, U.K., pp.1-5.



Didier, G., Wendt, H. and Abry, P. (2019), 'Detection and estimation of delays in bivariate self-similarity: bootstrapped complex wavelet coherence'. To appear in 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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