Free Access
Volume 21, 2017
Page(s) 275 - 302
Published online 12 December 2017
  1. H. Aguilaniu, L. Gustafsson, M. Rigoulet and T. Nyström, Asymmetric Inheritance of Oxidatively Damaged Proteins During Cytokinesis. Sci. 299 (2003) 1751. [CrossRef] [Google Scholar]
  2. M. Ackermann, S.C. Stearns and U. Jenal, Senescence in a Bacterium with Asymmetric Division. Sci. 300 (2003) 1920. [CrossRef] [Google Scholar]
  3. K.B. Athreya and P.E. Ney, Branching Processes. Springer edition (1970). [Google Scholar]
  4. V. Bansaye, Proliferating parasites in dividing cells: Kimmels branching model revisited. Ann. Appl. Probab. (2008) 967–996. [Google Scholar]
  5. V. Bansaye, J.-F. Delmas, L. Marsalle and V.C. Tran, Limit theorems for Markov processes indexed by continuous time Galton - Watson trees. Ann. Appl. Probab. 21 (2011). [Google Scholar]
  6. V. Bansaye and V.C. Tran, Branching Feller diffusion for cell division with parasite infection. ALEA, Lat. Am. J. Probab. Math. Stat. 8 (2011) 95–127. [Google Scholar]
  7. V. Bansaye, J.C. Pardo and C. Smadi, On the extinction of continuous state branching processes with catastrophes. Electron. J. Probab. 18 (2013) 1–31. [Google Scholar]
  8. B. Bercu, B. De Saporta and A. Gégout-Petit, Asymptotic analysis for bifurcating autoregressive processes via a martingale approach. Electron. J. Probab. 14 (2009) 2492–2526. [Google Scholar]
  9. K. Bertin, C. Lacour and V. Rivoirard, Adaptive pointwise estimation of conditional density function. Ann. Inst. Henri Poincaré Probab. Statist. (2015). [Google Scholar]
  10. S. Valère Bitseki Penda, Deviation inequalities for bifurcating Markov chains on Galton – Watson tree. ESAIM: PS 19 (2015) 689–724. [CrossRef] [EDP Sciences] [Google Scholar]
  11. B. Cloez, Limit theorems for some branching measure-valued processes. Adv. Appl. Probab. 49 (2017) 549–580. [Google Scholar]
  12. J.-F. Delmas and L. Marsalle, Detection of cellular aging in a Galton-Watson process. Stochastic Processes and their Application 120 (2010) 2495–2519. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Doumic, M. Hoffmann, N. Krell and L. Robert, Statistical estimation of a growth-fragmentation model observed on a genealogical tree. Bernoulli 21 1760–1799. [Google Scholar]
  14. M. Doumic, M. Hoffmann, P. Reynaud-Bouret and V. Rivoirard, Nonparametric estimation of the division rate of a size-structured population. SIAM J. Numer. Anal. 50 (2012). [Google Scholar]
  15. S.N. Evans and D. Steinsaltz, Damage segregation at fissioning may increase growth rates: A superprocess model. Theoret. Popul. Biol. 71 (2007) 473–490. [CrossRef] [Google Scholar]
  16. A. Goldenshluger and O. Lepski, Bandwidth selection in kernel density estimation: oracle inequalities and adaptive minimax optimality. Ann. Statist. 39 (2011) 1608–1632. [CrossRef] [Google Scholar]
  17. J. Guyon, Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann. Appl. Probab. 17 (2007) 1538–1569. [Google Scholar]
  18. T.E. Harris, The Theory of Branching Processes. Springer, Berlin (1963). [Google Scholar]
  19. V.H. Hoang, Adaptive estimation for inverse problems with applications to cell divisions. PhD dissertation, Université de Lille 1 Sciences et Technologies, (2016). [Google Scholar]
  20. M. Hoffmann and A. Olivier, Nonparametric estimation of the division rate of an age dependent branching process. Stoch. Process. Appl. 126 (2016) 1433–1471. [CrossRef] [Google Scholar]
  21. N. Ikeda and S. Wanatabe, Stochastic differential equations and diffusion processes. Vol. 24 of North-Holland Mathematical Library. [Google Scholar]
  22. J. Jacob and A.N. Shiryaev, Limit Theorems for Stochastic Processes. Springer Verlag, Berlin (1987). [Google Scholar]
  23. C.-Y. Lai, E. Jaruga, C. Borghouts and S.M. Jazwinski1, A Mutation in the ATP2 Gene Abrogates the Age Asymmetry Between Mother and Daughter Cells of the Yeast Saccharomyces cerevisiae. Genetics 162 (2002) 73–87. [PubMed] [Google Scholar]
  24. C. Lacour and P. Massart. Minimal penalty for Goldenshluger-Lepski method. Stoch. Process. Appl. 126 (2016) 3774–3789. [CrossRef] [Google Scholar]
  25. 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. PNAS 105 (2015) 3076–3081. [CrossRef] [Google Scholar]
  26. P. Massart, Concentration Inequalities and Model Selection. Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour, 6-23 (2003). Springer (2007). [Google Scholar]
  27. S.P. Meyn and R.L. Tweedie, Stability of Markovian processes iii: Foster - Lyapunov criteria for continuous-time processes. Adv. Appl. Probab. 25 (1993). [Google Scholar]
  28. J.B. Moseley, Cellular Aging: Symmetry Evades Senescence. Current Biology, Vol. 23, Issue 19, R871 R873 (2013). [Google Scholar]
  29. J. Peter, A general stochastic model for population development. Scandinavian Actuarial J. 1969 (1969) 84–103. [Google Scholar]
  30. L. Robert, M. Hoffmann, N. Krell, S. Aymerich, J. Robert and M. Doumic, Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism. BMC Biology 12 (2014). [Google Scholar]
  31. Sh.M. Ross, Stochastic Processes. Wiley, 2nd edition (1995). [Google Scholar]
  32. P. Reynaud-Bouret, V. Rivoirard, F. Grammont and C. Tuleau-Malot, Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis. J. Math. Neuroscience 4 (2014). [CrossRef] [Google Scholar]
  33. B.W. Silverman, Density estimation for statistics and data analysis, volume 26. CRC press (1986). [Google Scholar]
  34. E.J. Stewart, R. Madden, G. Paul and F. Taddei, Aging and Death in an Organism That Reproduces by Morphologically Symmetric Division. PLOS Biology 3 (2005). [Google Scholar]
  35. V.C. Tran, Modèles particulaires stochastiques pour des problèmes d’évolution adaptive et pour l’approximation de solutions statisques. Ph.D. dissertation, Université Paris X - Nanterre, (2006). [Google Scholar]
  36. V.C. Tran, Large population limit and time behaviour of a stochastic particle model describing an age-structured population. ESAIM: Probab. Statis. 12 (2008). [Google Scholar]
  37. A.B. Tsybakov, Introduction to Nonparametric Estimation. Springer series in Statistics. Springer (2004). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.