M. Ackermann, S. C. Stearns, and U. Jenal, Senescence in a Bacterium with Asymmetric Division, Science, vol.300, issue.5627, pp.1920-1920, 2003.
DOI : 10.1126/science.1083532

H. Aguilaniu, L. Gustafsson, M. Rigoulet, and T. Nyström, Asymmetric Inheritance of Oxidatively Damaged Proteins During Cytokinesis, Science, vol.299, issue.5613, pp.1751-1753, 2003.
DOI : 10.1126/science.1080418

D. Aldous, Stopping times and tightness. The Annals of Probability, pp.335-340, 1978.
DOI : 10.1214/aop/1176995579

R. B. Arellano-valle, H. Bolfarine, and L. Gasco, Measurement Error Models with Nonconstant Covariance Matrices, Journal of Multivariate Analysis, vol.82, issue.2, pp.395-415, 2002.
DOI : 10.1006/jmva.2001.2024
URL : http://doi.org/10.1006/jmva.2001.2024

K. B. Athreya and P. E. Ney, Branching processes, 2012.
DOI : 10.1007/978-3-642-65371-1

A. Bakushinskii, On the construction of regularizing algorithms under random noise, Soviet Math. Doklady, pp.231-233, 1969.

V. Bansaye, Proliferating parasites in dividing cells: Kimmel's branching model revisited. The Annals of Applied Probability, pp.967-996, 2008.
DOI : 10.1214/07-aap465

V. Bansaye, J. Delmas, L. Marsalle, and V. C. Tran, Limit theorems for Markov processes indexed by continuous time Galton???Watson trees, The Annals of Applied Probability, vol.21, issue.6, 2011.
DOI : 10.1214/10-AAP757
URL : https://hal.archives-ouvertes.fr/hal-00431118

V. Bansaye and S. Méléard, Some stochastic models for structured populations : scaling limits and long time behavior, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01162547

V. Bansaye, J. C. Millan, and C. Smadi, On the extinction of continuous state branching processes with catastrophes, Electronic Journal of Probability, vol.18, issue.0, pp.181-212, 2013.
DOI : 10.1214/EJP.v18-2774
URL : https://hal.archives-ouvertes.fr/hal-00781203

V. Bansaye, V. C. Tran, A. Lat, . J. Am, B. Probab et al., Branching feller diffusion for cell division with parasite infection Asymptotic analysis for bifurcating autoregressive processes via a martingale approach, Math. Stat. Electronic Journal of Probability, vol.8, issue.87, pp.142492-2526, 2009.

M. Bertero and P. Boccacci, Introduction to inverse problems in imaging, 1998.
DOI : 10.1887/0750304359

K. Bertin, C. Lacour, and V. Rivoirard, Adaptive pointwise estimation of conditional density function, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.52, issue.2, pp.939-980, 2016.
DOI : 10.1214/14-AIHP665
URL : https://hal.archives-ouvertes.fr/hal-00922555

N. Bissantz and H. Holzmann, Statistical inference for inverse problems, Inverse Problems, vol.24, issue.3, p.34009, 2008.
DOI : 10.1088/0266-5611/24/3/034009
URL : http://dx.doi.org/10.17877/DE290R-14175

T. Bourgeron, M. Doumic, and M. Escobedo, Estimating the division rate of the growth-fragmentation equaion with a self-similar kernel, Inverse Problems, vol.30, 2014.

A. Calsina and M. Sanchón, Stability and instability of equilibria of an equation of size structured population dynamics, Journal of Mathematical Analysis and Applications, vol.286, issue.2, pp.435-452, 2003.
DOI : 10.1016/S0022-247X(03)00464-5

R. J. Carroll, A. Delaigle, and P. Hall, Nonparametric Prediction in Measurement Error Models, Journal of the American Statistical Association, vol.104, issue.487, pp.993-1003, 2009.
DOI : 10.1198/jasa.2009.tm07543

L. Cavalier, Nonparametric statistical inverse problems, Inverse Problems, vol.24, issue.3, p.34004, 2008.
DOI : 10.1088/0266-5611/24/3/034004
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.5900

L. Cavalier and N. W. Hengartner, Adaptive estimation for inverse problems with noisy operators, Inverse Problems, vol.21, issue.4, p.1345, 2005.
DOI : 10.1088/0266-5611/21/4/010

G. Chagny, Goldenshluger???????Lepski strategies in warped bases regression, ESAIM: Probability and Statistics, vol.17, pp.328-358, 2013.
DOI : 10.1051/ps/2011165

C. Chesneau, On adaptive wavelet estimation of the regression function and its derivatives in an errors-in-variables model, Curr. Dev. Theory Appl. Wavelets, vol.4, issue.2, pp.185-208, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00466830

M. Chichignoud, V. H. Hoang, T. M. Pham-ngoc, and V. Rivoirard, Adaptive wavelet multivariate regression with errors in variables, Electronic Journal of Statistics, vol.11, issue.1, 2016.
DOI : 10.1214/17-EJS1238
URL : https://hal.archives-ouvertes.fr/hal-01253508

B. Cloez, Limit theorems for some branching measure-valued processes. arXiv preprint, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00598030

F. Comte, V. Genon-catalot, and A. Samson, Nonparametric estimation for stochastic differential equations with random effects, Stochastic Processes and their Applications, pp.2522-2551, 2013.
DOI : 10.1016/j.spa.2013.04.009
URL : https://hal.archives-ouvertes.fr/hal-00761394

F. Comte and C. Lacour, Data-driven density estimation in the presence of additive noise with unknown distribution, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.18, issue.4, pp.601-627, 2011.
DOI : 10.1111/j.1467-9868.2011.00775.x

F. Comte and C. Lacour, Anisotropic adaptive kernel deconvolution, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.49, issue.2, pp.569-609, 2013.
DOI : 10.1214/11-AIHP470
URL : https://hal.archives-ouvertes.fr/hal-00579608

F. Comte, A. Samson, and J. J. Stirnemann, Deconvolution Estimation of Onset of Pregnancy with Replicate Observations, Scandinavian Journal of Statistics, vol.321, issue.7271, pp.325-345, 2014.
DOI : 10.1111/sjos.12029
URL : https://hal.archives-ouvertes.fr/hal-00588235

F. Comte and M. Taupin, Adaptive estimation in a nonparametric regression model with errors-in-variables, Statist. Sinica, vol.17, issue.3, pp.1065-1090, 2007.

D. , D. Canditiis, and M. Pensky, Simultaneous wavelet deconvolution in periodic setting, Scandinavian Journal of Statistics, vol.33, issue.2, pp.293-306, 2006.

A. Delaigle, P. Hall, and F. Jamshidi, Confidence bands in non-parametric errors-in-variables regression, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.1, pp.149-169, 2015.
DOI : 10.1111/rssb.12067

A. Delaigle, P. Hall, and H. Müller, Accelerated convergence for nonparametric regression with coarsened predictors. The Annals of Statistics, pp.2639-2653, 2007.
DOI : 10.1214/009053607000000497
URL : http://arxiv.org/abs/0803.3017

A. Delaigle and A. Meister, Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem, Journal of the American Statistical Association, vol.102, issue.480, pp.1416-1426, 2007.
DOI : 10.1198/016214507000000987

J. Delmas and L. Marsalle, Detection of cellular aging in a Galton???Watson process, Stochastic Processes and their Applications, pp.2495-2519, 2010.
DOI : 10.1016/j.spa.2010.07.002
URL : https://hal.archives-ouvertes.fr/hal-00293422

O. Diekmann, M. Gyllenberg, J. J. Metz, and R. H. Thieme, On the formulation and analysis of general deterministic structured population models, Journal of Mathematical Biology, vol.36, issue.4, pp.349-388, 1998.
DOI : 10.1007/s002850050104

S. Donnet and A. Samson, Estimation of parameters in incomplete data models defined by dynamical systems, Journal of Statistical Planning and Inference, vol.137, issue.9, pp.2815-2831, 2007.
DOI : 10.1016/j.jspi.2006.10.013
URL : https://hal.archives-ouvertes.fr/hal-00263507

M. Doumic and P. Gabriel, EIGENELEMENTS OF A GENERAL AGGREGATION-FRAGMENTATION MODEL, Mathematical Models and Methods in Applied Sciences, vol.20, issue.05, pp.757-783, 2010.
DOI : 10.1142/S021820251000443X
URL : https://hal.archives-ouvertes.fr/hal-00408088

M. Doumic, M. Hoffmann, N. Krell, and L. Robert, Statistical estimation of a growth-fragmentation model observed on a genealogical tree, Bernoulli, vol.21, issue.3, pp.1760-1799, 2015.
DOI : 10.3150/14-BEJ623
URL : https://hal.archives-ouvertes.fr/hal-01102799

M. Doumic, M. Hoffmann, P. Reynaud-bouret, and V. Rivoirard, Nonparametric Estimation of the Division Rate of a Size-Structured Population, SIAM Journal on Numerical Analysis, vol.50, issue.2, pp.925-950, 2012.
DOI : 10.1137/110828344
URL : https://hal.archives-ouvertes.fr/hal-00578694

M. Doumic, B. Perthame, and J. P. Zubelli, Numerical solution of an inverse problem in size-structured population dynamics, Inverse Problems, vol.25, issue.4, p.45008, 2009.
DOI : 10.1088/0266-5611/25/4/045008
URL : https://hal.archives-ouvertes.fr/hal-00327151

M. Doumic and L. M. Tine, Estimating the division rate for the growth-fragmentation equation, Journal of Mathematical Biology, vol.23, issue.1, pp.69-103, 2013.
DOI : 10.1007/s00285-012-0553-6
URL : https://hal.archives-ouvertes.fr/hal-00634539

L. Du, C. Zou, and Z. Wang, Nonparametric regression function estimation for errors-in-variables models with validation data, Statistica Sinica, vol.21, issue.3, pp.1093-1113, 2011.
DOI : 10.5705/ss.2009.047

S. N. Ethier and T. G. Kurtz, Markov processes: characterization and convergence, 2009.
DOI : 10.1002/9780470316658

S. N. Evans and D. Steinsaltz, Damage segregation at fissioning may increase growth rates: A superprocess model, Theoretical Population Biology, vol.71, issue.4, pp.473-490, 2007.
DOI : 10.1016/j.tpb.2007.02.004
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2430589

J. Fan and J. Koo, Wavelet deconvolution, IEEE Trans. Inform. Theory, vol.48, issue.3, pp.734-747, 2002.

J. Fan and E. Masry, Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes, Journal of Multivariate Analysis, vol.43, issue.2, pp.237-271, 1992.
DOI : 10.1016/0047-259X(92)90036-F

J. Fan and Y. K. Truong, Nonparametric Regression with Errors in Variables, The Annals of Statistics, vol.21, issue.4, pp.1900-1925, 1993.
DOI : 10.1214/aos/1176349402
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.6441

J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, Journal of Mathematical Analysis and Applications, vol.328, issue.1, pp.119-136, 2007.
DOI : 10.1016/j.jmaa.2006.05.032

R. Ferrière and V. C. Tran, Stochastic and deterministic models for age-structured populations with genetically variable traits, ESAIM: Proceedings, vol.27, pp.289-310, 2009.
DOI : 10.1051/proc/2009033

N. Fournier and S. Méléard, A microscopic probabilistic description of a locally regulated population and macroscopic approximations, The Annals of Applied Probability, vol.14, issue.4, pp.1880-1919, 2004.
DOI : 10.1214/105051604000000882

F. Gach, R. Nickl, and V. Spokoiny, Spatially adaptive density estimation by localised Haar projections, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.49, issue.3, pp.900-914, 2013.
DOI : 10.1214/12-AIHP485
URL : http://arxiv.org/abs/1111.2807

A. Goldenshluger and O. Lepski, Universal pointwise selection rule in multivariate function estimation, Bernoulli, vol.14, issue.4, pp.1150-1190, 2008.
DOI : 10.3150/08-BEJ144

A. Goldenshluger and O. Lepski, Bandwidth selection in kernel density estimation: orcale inequalities and adaptive minimax optimality. The Annals of Statistics, pp.1608-1632, 2011.

J. Guyon, Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging, The Annals of Applied Probability, vol.17, issue.5/6, pp.1538-1569, 2007.
DOI : 10.1214/105051607000000195

T. E. Harris, The theory of branching processes, 1963.
DOI : 10.1007/978-3-642-51866-9

V. H. Hoang, Estimating the division kernel of a size-structured population, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01196427

M. Hoffmann and A. Olivier, Nonparametric estimation of the division rate of an age dependent branching process, Stochastic Processes and their Applications, pp.1433-1471, 2016.
DOI : 10.1016/j.spa.2015.11.009
URL : https://hal.archives-ouvertes.fr/hal-01254203

R. A. Horn, The hadamard product, Proc. Symp. Appl. Math, pp.87-169, 1990.

C. Houdre, P. Reynaud, and . Bouret, Exponential Inequalities, with Constants, for U-statistics of Order Two, pp.55-60
DOI : 10.1007/978-3-0348-8069-5_5

J. T. Hwang, Multiplicative errors-in-variables models with applications to recent data released by the us department of energy, Journal of the American Statistical Association, issue.395, pp.81680-688, 1986.

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes

D. A. Ioannides and P. D. , Nonparametric regression with errors in variables and applications, Statistics & Probability Letters, vol.32, issue.1, pp.35-43, 1997.
DOI : 10.1016/S0167-7152(96)00054-5

J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, 1987.
DOI : 10.1007/978-3-662-02514-7

K. P. Jagdish and B. Campbell, Handbook of the normal distribution, 1996.

P. Jagers, A general stochastic model for population development, Scandinavian Actuarial Journal, vol.1, issue.1-2, pp.84-103, 1969.
DOI : 10.1080/03461238.1969.10405220

A. Joffe and M. Métivier, Weak convergence of sequences of semimartingales with applications to multitype branching processes, Advances in Applied Probability, pp.20-65, 1986.

I. M. Johnstone, G. Kerkyacharian, D. Picard, and M. Raimondo, Wavelet deconvolution in a periodic setting, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.11, issue.3, pp.547-573, 2004.
DOI : 10.1081/NFA-120003678
URL : https://hal.archives-ouvertes.fr/hal-00102266

J. Kalifa and S. Mallat, Thresholding estimators for linear inverse problems and deconvolutions, Annals of Statistics, vol.31, issue.1, pp.58-109, 2003.

G. Kerkyacharian, D. Picard, and M. Raimondo, Adaptive boxcar deconvolution on full lebesgue measure sets, Statistica Sinica, vol.17, issue.1, pp.317-340, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00160979

J. Koo and K. Lee, B-spline estimation of regression functions with errors in variable, Statistics & Probability Letters, vol.40, issue.1, pp.57-66, 1998.
DOI : 10.1016/S0167-7152(98)00098-4

C. Lacour and P. Massart, Minimal penalty for Goldenshluger???Lepski method, Stochastic Processes and their Applications, 2016.
DOI : 10.1016/j.spa.2016.04.015
URL : https://hal.archives-ouvertes.fr/hal-01121989

C. Lai, E. Jaruga, C. Borghouts, and S. M. Jazwinski, A mutation in the atp2 gene abrogates the age asymmetry between mother and daughter cells of the yeast saccharomyces cerevisiae, Genetics, vol.162, issue.1, pp.73-87, 2002.

A. B. Lindner, R. Madden, A. Demarez, E. J. Stewart, and F. Taddei, Asymmetric segregation of protein aggregates is associated with cellular aging and rejuvenation, Proceedings of the National Academy of Sciences, pp.3076-3081, 2008.
DOI : 10.1073/pnas.0708931105

O. Linton and Y. Whang, NONPARAMETRIC ESTIMATION WITH AGGREGATED DATA, Econometric Theory, vol.18, issue.02, pp.420-468, 2002.
DOI : 10.1017/S0266466602182089
URL : http://eprints.lse.ac.uk/2092/1/Nonparametric_Estimation_with_Aggregated_Data.pdf

B. P. Loh and M. J. Wainwright, High-dimensional regression with noisy and missing data: provable guarantees wth nonconvexity. The Annals of Statistics, pp.1637-1664, 2012.
DOI : 10.1214/12-aos1018
URL : http://arxiv.org/abs/1109.3714

P. Massart, Concentration Inequalities and Model Selection. Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour, pp.6-23, 2003.

A. Meister, Deconvolution problems in nonparametric statistics, Lecture Notes in Statistics, vol.193, 2009.
DOI : 10.1007/978-3-540-87557-4

S. Méléard and S. Roelly, Sur les convergences étroite ou vague de processus à valeur mesures. Comptes Rendus de l'Academie des Sciences, Serie I 317, 1993.

S. Méléard and V. C. Tran, Slow and fast scales for superprocess limits of age-structured populations, Stochastic Processes and their Applications, 2012.

S. P. Meyn and R. L. Tweedie, Stability of markovian processes iii: Fosterlyapunov criteria for continuous-time processes, Advances in Applied Probability, pp.518-548, 1993.

P. Michel, EXISTENCE OF A SOLUTION TO THE CELL DIVISION EIGENPROBLEM, Mathematical Models and Methods in Applied Sciences, vol.16, issue.supp01, pp.1125-1153, 2006.
DOI : 10.1142/S0218202506001480

P. Michel, S. Mischler, and B. Perthame, General relative entropy inequality: an illustration on growth models, Journal de Math??matiques Pures et Appliqu??es, vol.84, issue.9, pp.1235-1260, 2005.
DOI : 10.1016/j.matpur.2005.04.001
URL : http://doi.org/10.1016/j.matpur.2005.04.001

K. Mosegaard and A. Tarantola, Probabilistic approach to inverse problems In International Handbook of Earthquake and Engineering Seismology, 2002.

J. B. Moseley, Cellular Aging: Symmetry Evades Senescence, Current Biology, vol.23, issue.19, pp.871-873, 2013.
DOI : 10.1016/j.cub.2013.08.013
URL : http://doi.org/10.1016/j.cub.2013.08.013

M. H. Neumann, On the effect of estimating the error density in nonparametric deconvolution, Journal of Nonparametric Statistics, vol.46, issue.4, pp.307-330, 1997.
DOI : 10.1214/aos/1176348768

D. V. Nguyen, D. ?entürk, and R. J. Carroll, Covariate-adjusted linear mixed effects model with an application to longitudinal data, Journal of Nonparametric Statistics, vol.54, issue.6, pp.459-481, 2008.
DOI : 10.1046/j.1523-1755.2002.00076.x

S. V. Penda, Deviation inequalities for bifurcating Markov chains on Galton???Watson tree, ESAIM: Probability and Statistics, vol.19, pp.689-724, 2015.
DOI : 10.1051/ps/2015007
URL : https://hal.archives-ouvertes.fr/hal-00789557

M. Pensky and T. Sapatinas, Functional deconvolution in a periodic setting: uniform case. The Annals of Statistics, pp.73-104, 2009.

B. Perthame, Transport equations arising in biology, Frontiers in Mathematics. Birchkhauser, 2007.

B. Perthame and L. Ryzhik, Exponential decay for the fragmentation or cell-division equation, Journal of Differential Equations, vol.210, issue.1, pp.155-177, 2005.
DOI : 10.1016/j.jde.2004.10.018

R. Reams, Hadamard inverses, square roots and products of almost semidefinite matrices, Linear Algebra and its Applications, vol.288, pp.35-43, 1999.
DOI : 10.1016/S0024-3795(98)10162-3

P. Reynaud-bouret, V. Rivoirard, F. Grammont, and C. Tuleau-malot, Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis, The Journal of Mathematical Neuroscience, vol.4, issue.1, p.1, 2014.
DOI : 10.1109/TIT.1981.1056305
URL : https://hal.archives-ouvertes.fr/hal-00789127

L. Robert, M. Hoffmann, N. Krell, S. Aymerich, J. Robert et al., Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism, BMC Biology, vol.12, issue.1, p.1, 2014.
DOI : 10.1088/0266-5611/25/4/045008
URL : https://hal.archives-ouvertes.fr/hal-00981312

S. M. Ross, Stochastic processes, 1996.

A. Samson and M. Thieullen, A contrast estimator for completely or partially observed hypoelliptic diffusion, Stochastic Processes and their Applications, pp.2521-2552, 2012.
DOI : 10.1016/j.spa.2012.04.006
URL : https://hal.archives-ouvertes.fr/hal-00714352

B. W. Silverman, Density estimation for statistics and data analysis, 1986.
DOI : 10.1007/978-1-4899-3324-9

E. J. Stewart, R. Madden, G. Paul, and F. Taddei, Aging and Death in an Organism That Reproduces by Morphologically Symmetric Division, PLoS Biology, vol.297, issue.2, 2005.
DOI : 10.1371/journal.pbio.0030045.sv001
URL : https://hal.archives-ouvertes.fr/inserm-00080154

J. Stirnemann, F. Comte, and A. Samson, Density estimation of a biomedical variable subject to measurement error using an auxiliary set of replicate observations, Statistics in Medicine, vol.117, issue.8, pp.314154-4163, 2012.
DOI : 10.1002/sim.5392
URL : https://hal.archives-ouvertes.fr/hal-00687606

V. Sudakov and L. Khalfin, Statistical approach to correctness of problems in mathematical physics, DOKLADY AKADEMII NAUK SSSR, vol.157, issue.5, p.1058, 1964.

A. Tarantola, Inverse problem theory and methods for model parameter estimation . siam, 2005.
DOI : 10.1137/1.9780898717921

A. N. Tikhonov, Regularization of incorrectly posed problems, SOVIET MATHEMATICS DOKLADY, 1963.

A. N. Tikhonov and V. Y. Arsenin, Solutions of ill-posed problems, 1977.

V. C. Tran, Modèles particulaires stochastiques pour des problèmes d'évolution adaptive et pour l'approximation de solutions statisques, 2006.

V. C. Tran, Large population limit and time behaviour of a stochastic particle model describing an age-structured population, ESAIM: Probability and Statistics, vol.12, 2008.
DOI : 10.1051/ps:2007052
URL : https://hal.archives-ouvertes.fr/hal-00122191

V. C. Tran, Une ballade en forêts aléatoires : Théorèmes limites pour des populations structurées et leurs généalogies, étude probabiliste et statistique de modèles SIR en épidémiologie, contributions à la géométrie aléatoire, 2014.

A. B. Tsybakov, Introduction to Nonparametric Estimation. Springer series in Statistics, 2009.

A. S. Whittemore and J. B. Keller, Approximations for Regression with Covariate Measurement Error, Journal of the American Statistical Association, vol.10, issue.404, pp.1057-1066, 1988.
DOI : 10.1080/01621459.1988.10478701

L. Wu, Exact and Approximate Inferences for Nonlinear Mixed-Effects Models With Missing Covariates, Journal of the American Statistical Association, vol.99, issue.467, pp.700-709, 2004.
DOI : 10.1198/016214504000001006