D. W. Austin, M. S. Allen, J. M. Mccollum, R. D. Dar, J. R. Wilgus et al., Gene network shaping of inherent noise spectra, Nature, issue.7076, pp.439608-439619, 2006.

M. Bertero, Linear inverse and iii-posed problems Advances in Electronics and Electron Physics, pp.1-120, 1989.
DOI : 10.1016/s0065-2539(08)60946-4

C. G. Bowsher, M. Voliotis, and P. S. Swain, The Fidelity of Dynamic Signaling by Noisy Biomolecular Networks, PLoS Computational Biology, vol.102, issue.4, p.1002965, 2013.
DOI : 10.1371/journal.pcbi.1002965.s001

S. Boyd and L. Vandenberghe, Convex Optimization, 2004.

J. Chiì-es and P. Delfiner, Geostatistics ? Modelling Spatial Uncertainty, 1999.

E. Cinquemani, Reconstructing Statistics of Promoter Switching from Reporter Protein Population Snapshot Data, Proceedings of the fourth international workshop on Hybrid Systems Biology, pp.3-19
DOI : 10.1007/978-3-319-26916-0_1

URL : https://hal.archives-ouvertes.fr/hal-01218004

E. Cinquemani, Reconstruction of promoter activity statistics from reporter protein population snapshot data, 2015 54th IEEE Conference on Decision and Control (CDC), pp.1471-1476, 2015.
DOI : 10.1109/CDC.2015.7402418

URL : https://hal.archives-ouvertes.fr/hal-01218010

E. Cinquemani, On Observability and Reconstruction of Promoter Activity Statistics from Reporter Protein Mean and Variance Profiles, Proceedings of the fifth international workshop on Hybrid Systems Biology, pp.147-163
DOI : 10.1093/bioinformatics/btv246

URL : https://hal.archives-ouvertes.fr/hal-01399934

E. Cinquemani, A. Milias-argeitis, S. Summers, and J. Lygeros, Local Identification of Piecewise Deterministic Models of Genetic Networks, LNCS, vol.39, issue.4, pp.105-119, 2009.
DOI : 10.1007/s11075-004-6709-8

C. D. Cox, J. M. Mccollum, D. W. Austin, M. S. Allen, R. D. Dar et al., Frequency domain analysis of noise in simple gene circuits, 2006. [11] CVX Research, Inc. CVX: Matlab software for disciplined convex programming, 2012.
DOI : 10.1038/nature04588

G. De-nicolao, G. Sparacino, and C. Cobelli, Nonparametric input estimation in physiological systems: Problems, methods, and case studies, Automatica, vol.33, issue.5, pp.851-870, 1997.
DOI : 10.1016/S0005-1098(96)00254-3

B. Finkenstädt, E. A. Heron, M. Komorowski, K. Edwards, S. Tang et al., Reconstruction of transcriptional dynamics from gene reporter data using differential equations, Bioinformatics, vol.24, issue.24, pp.242901-2907, 2008.
DOI : 10.1093/bioinformatics/btn562

N. Friedman, L. Cai, and X. S. Xie, Linking Stochastic Dynamics to Population Distribution: An Analytical Framework of Gene Expression, Physical Review Letters, vol.81, issue.16, p.168302, 2006.
DOI : 10.1126/science.1109090

C. Gadgil, C. H. Lee, and H. G. Othmer, A stochastic analysis of first-order reaction networks, Bulletin of Mathematical Biology, vol.67, issue.5, pp.901-946, 2005.
DOI : 10.1016/j.bulm.2004.09.009

W. A. Gardner, Introduction to random processes with applications to signals and systems, Automatica, vol.24, issue.5, 1990.
DOI : 10.1016/0005-1098(88)90124-0

C. S. Gillespie, Moment-closure approximations for mass-action models, IET Systems Biology, vol.3, issue.1, pp.52-58, 2009.
DOI : 10.1049/iet-syb:20070031

D. T. Gillespie, A rigorous derivation of the chemical master equation, Physica A: Statistical Mechanics and its Applications, vol.188, issue.1-3, pp.404-425, 1992.
DOI : 10.1016/0378-4371(92)90283-V

C. W. Granger, Investigating Causal Relations by Econometric Models and Cross-spectral Methods, Econometrica, vol.37, issue.3, pp.424-438, 1969.
DOI : 10.2307/1912791

J. Hasenauer, S. Waldherr, M. Doszczak, N. Radde, P. Scheurich et al., Identification of models of heterogeneous cell populations from population snapshot data, BMC Bioinformatics, vol.12, issue.1, p.125, 2011.
DOI : 10.1038/sj.cdd.4401189

J. Hasenauer, V. Wolf, A. Kazeroonian, and F. J. Theis, Method of conditional moments (MCM) for the Chemical Master Equation, Journal of Mathematical Biology, vol.109, issue.21, pp.687-735, 2014.
DOI : 10.1073/pnas.1200161109

J. P. Hespanha, Modelling and analysis of stochastic hybrid systems, IEE Proceedings - Control Theory and Applications, vol.153, issue.5, pp.520-535, 2006.
DOI : 10.1049/ip-cta:20050088

A. Hilfinger, M. Chen, and J. Paulsson, Using Temporal Correlations and Full Distributions to Separate Intrinsic and Extrinsic Fluctuations in Biological Systems, Physical Review Letters, vol.109, issue.24, p.2012, 248104.
DOI : 10.1109/TAC.2007.911347

URL : http://doi.org/10.1103/physrevlett.109.248104

A. Hilfinger, T. M. Norman, G. Vinnicombe, and J. Paulsson, Constraints on Fluctuations in Sparsely Characterized Biological Systems, Physical Review Letters, vol.116, issue.5, pp.116-2016
DOI : 10.1038/nature12804

URL : https://doi.org/10.1103/physrevlett.116.058101

A. H. Jazwinski, Stochastic processes and filtering theory, 1970.

M. Kaern, T. C. Elston, W. J. Blake, and J. J. Collins, Stochasticity in gene expression: from theories to phenotypes, Nature Reviews Genetics, vol.8706, issue.6, pp.451-464, 2005.
DOI : 10.1073/pnas.0400673101

A. Klimovskaia, S. Ganscha, and M. Claassen, Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series, PLOS Computational Biology, vol.11, issue.6, pp.1-20
DOI : 10.1371/journal.pcbi.1005234.s016

M. Komorowski, B. Finkenstädt, C. Harper, and D. Rand, Bayesian inference of biochemical kinetic parameters using the linear noise approximation, BMC Bioinformatics, vol.10, issue.1, p.343, 2009.
DOI : 10.1186/1471-2105-10-343

M. Komorowski, B. Finkenstädt, and D. Rand, Using a Single Fluorescent Reporter Gene to Infer Half-Life of Extrinsic Noise and Other Parameters of Gene Expression, Biophysical Journal, vol.98, issue.12, pp.982759-2769, 2010.
DOI : 10.1016/j.bpj.2010.03.032

I. Lestas, G. Vinnicombe, and J. Paulsson, Fundamental limits on the suppression of molecular fluctuations, Nature, vol.26, issue.7312, pp.174-178, 2010.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

A. Lindquist and G. Picci, Linear stochastic systems ? A geometric approach to modeling, estimation and identification, 2015.

A. Llamosi, A. M. Gonzalez-vargas, C. Versari, E. Cinquemani, G. Ferrari-trecate et al., What Population Reveals about Individual Cell Identity: Single-Cell Parameter Estimation of Models of Gene Expression in Yeast, PLOS Computational Biology, vol.10, issue.2, p.1004706, 2016.
DOI : 10.1371/journal.pcbi.1004706.s011

URL : https://hal.archives-ouvertes.fr/hal-01248298

J. Lygeros and M. Prandini, Stochastic Hybrid Systems: A Powerful Framework for Complex, Large Scale Applications, European Journal of Control, vol.16, issue.6, pp.583-594, 2010.
DOI : 10.3166/ejc.16.583-594

B. Munsky, B. Trinh, and M. Khammash, Listening to the noise: random fluctuations reveal gene network parameters, Molecular Systems Biology, vol.9, issue.318, 2009.
DOI : 10.1006/plas.2000.1477

URL : http://msb.embopress.org/content/msb/5/1/318.full.pdf

G. Neuert, B. Munsky, R. Z. Tan, L. Teytelman, M. Khammash et al., Systematic identification of signal-activated stochastic gene regulation Number 2 in Cambridge series on statistical and probabilistic mathematics, Science J.R. Norris. Markov Chains, vol.33937, issue.6119, pp.584-587, 1997.

A. Ocone, L. Haghverdi, N. S. Mueller, and F. J. Theis, Reconstructing gene regulatory dynamics from high-dimensional single-cell snapshot data, Bioinformatics, vol.31, issue.12, pp.31-89, 2015.
DOI : 10.1093/bioinformatics/btv257

URL : https://academic.oup.com/bioinformatics/article-pdf/31/12/i89/17102147/btv257.pdf

E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman, and A. Van-oudenaarden, Regulation of noise in the expression of a single gene, Nature Genetics, vol.31, issue.1, pp.69-73, 2002.
DOI : 10.1038/ng869

J. Paulsson, Models of stochastic gene expression, Physics of Life Reviews, vol.2, issue.2, pp.157-175, 2005.
DOI : 10.1016/j.plrev.2005.03.003

J. M. Pedraza and A. Van-oudenaarden, Noise Propagation in Gene Networks, Science, vol.307, issue.5717, pp.1965-1969, 2005.
DOI : 10.1126/science.1109090

G. Pillonetto and B. M. Bell, Bayes and empirical Bayes semi-blind deconvolution using eigenfunctions of a prior covariance, Automatica, vol.43, issue.10, pp.1698-1712, 2007.
DOI : 10.1016/j.automatica.2007.02.025

A. Raj and A. Van-oudenaarden, Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences, Cell, vol.135, issue.2, pp.216-226, 2008.
DOI : 10.1016/j.cell.2008.09.050

URL : https://doi.org/10.1016/j.cell.2008.09.050

C. E. Rasmussen and C. K. Williams, Gaussian Processes in Machine Learning, 2006.
DOI : 10.1162/089976602317250933

URL : http://mlg.eng.cam.ac.uk/pub/pdf/Ras04.pdf

J. Ruess, A. Milias-argeitis, S. Summers, and J. Lygeros, Moment estimation for chemically reacting systems by extended Kalman filtering, The Journal of Chemical Physics, vol.19, issue.16, p.165102, 2011.
DOI : 10.1063/1.3103264

K. R. Sanft, S. Wu, M. Roh, J. Fu, R. K. Lim et al., StochKit2: software for discrete stochastic simulation of biochemical systems with events, Bioinformatics, vol.27, issue.17, pp.272457-2458, 2011.
DOI : 10.1093/bioinformatics/btr401

M. Schelker, A. Raue, J. Timmer, and C. Kreutz, Comprehensive estimation of input signals and dynamics in biochemical reaction networks, Bioinformatics, vol.28, issue.18, pp.529-534, 2012.
DOI : 10.1093/bioinformatics/bts393

M. L. Simpson, C. D. Cox, and G. S. Sayler, Frequency domain analysis of noise in autoregulated gene circuits, Proceedings of the National Academy of Sciences, vol.114, issue.1, pp.4551-4556, 2003.
DOI : 10.1016/0022-2836(77)90279-0

A. Singh and J. P. Hespanha, Approximate Moment Dynamics for Chemically Reacting Systems, IEEE Transactions on Automatic Control, vol.56, issue.2, pp.414-418, 2011.
DOI : 10.1109/TAC.2010.2088631

URL : http://www.ece.ucsb.edu/~hespanha/published/singh_transaction.pdf

T. Södeström and P. Stoica, System Identification, 1989.

D. M. Suter, N. Molina, D. Gatfield, K. Schneider, U. Schibler et al., Mammalian Genes Are Transcribed with Widely Different Bursting Kinetics, Science, vol.38, issue.1, pp.472-474, 2011.
DOI : 10.1146/annurev.biophys.050708.133728

URL : http://science.sciencemag.org/content/sci/332/6028/472.full.pdf

P. S. Swain, M. B. Elowitz, and E. D. Siggia, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proceedings of the National Academy of Sciences, vol.405, issue.6786, pp.9912795-12800, 2002.
DOI : 10.1038/35014651

M. Thattai and A. Van-oudenaarden, Intrinsic noise in gene regulatory networks, Proceedings of the National Academy of Sciences, vol.81, issue.3, pp.988614-8619, 2001.
DOI : 10.1021/j100540a008

URL : http://www.pnas.org/content/98/15/8614.full.pdf

G. Wahba, Spline models for observational data, SIAM, 1990.
DOI : 10.1137/1.9781611970128

X. Wang, B. Errede, and T. C. Elston, Mathematical Analysis and Quantification of Fluorescent Proteins as Transcriptional Reporters, Biophysical Journal, vol.94, issue.6, pp.2017-2026, 2008.
DOI : 10.1529/biophysj.107.122200

E. Yeung, J. L. Beck, and R. M. Murray, Modeling environmental disturbances with the chemical master equation, 52nd IEEE Conference on Decision and Control, pp.1384-1391, 2013.
DOI : 10.1109/CDC.2013.6760076

C. Zechner, J. Ruess, P. Krenn, S. Pelet, M. Peter et al., Moment-based inference predicts bimodality in transient gene expression, Proceedings of the National Academy of Sciences, vol.153, issue.8, pp.8340-8345, 2012.
DOI : 10.1049/ip-cta:20050088

URL : http://www.pnas.org/content/109/21/8340.full.pdf

C. Zechner, M. Unger, S. Pelet, M. Peter, and H. Koeppl, Scalable inference of heterogeneous reaction kinetics from pooled single-cell recordings, Nature Methods, vol.92, issue.2, pp.197-202, 2014.
DOI : 10.1109/78.978383

V. Zulkower, M. Page, D. Ropers, J. Geiselmann, H. De et al., Robust reconstruction of gene expression profiles from reporter gene data using linear inversion, Bioinformatics, vol.31, issue.12, pp.31-71, 2015.
DOI : 10.1093/bioinformatics/btv246

URL : https://hal.archives-ouvertes.fr/hal-01217800