Free Access
Issue
ESAIM: PS
Volume 19, 2015
Page(s) 689 - 724
DOI https://doi.org/10.1051/ps/2015007
Published online 11 December 2015
  1. K.B. Athreya, Large deviations for branching processes-I. Single type case. Ann. Appl. Probab. 5 (1994) 779–790 [CrossRef] [Google Scholar]
  2. K.B. Athreya and P.E Ney, Branching Process. Springer, Berlin (1972). [Google Scholar]
  3. K. Azuma, Weighted sums of certain dependent random variables. Tôhoku Math. J. 19 (1967) 357–367. [CrossRef] [Google Scholar]
  4. 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) 2263–2314 [CrossRef] [Google Scholar]
  5. G. Bennett, Probability inequalities for sum of independant random variables. J. Am. Stat. Assoc.57 (1962) 33–45. [Google Scholar]
  6. B. Bercu, and V. Blandin, A Rademacher−Menchov approach for randon coefficient bifurcating autoregressive processes. Stochastic Processes Appl. 125 (2015) 1218–1243. [CrossRef] [Google Scholar]
  7. B. Bercu, B. De Saporta and A. Gégout-Petit, Asymptotic analysis for bifurcating autoregressive processes via a martingale approach. Electronic. J. Probab. 14 (2009) 2492–2526. [Google Scholar]
  8. S.V. Bitseki Penda and H. Djellout, Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models. Ann. Inst. Henri Poincaré 50 (2014) 806–844. [CrossRef] [MathSciNet] [Google Scholar]
  9. S.V. Bitseki Penda, H. Djellout and A. Guillin, Deviation inequalities, Moderate deviations and some limit theorems for bifurcating Markov chains with application. Ann. Appl. Probab. 24 (2014) 235–291. [CrossRef] [Google Scholar]
  10. V. Blandin, Asymptotic results for random coefficient bifurcating autoregressive processes. Statistics 48 (2013) 1202–1232. [CrossRef] [Google Scholar]
  11. R. Cowan and R.G. Staudte, The bifurcating autoregressive model in cell lineage studies. Biometrics 42 (1986) 769–783. [CrossRef] [PubMed] [Google Scholar]
  12. B. De Saporta, A. Gégout-Petit and L. Marsalle, Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. Electron. J. Stat. 5 (2011) 1313–1353. [CrossRef] [Google Scholar]
  13. B. De Saporta, A. Gégout-Petit and L. Marsalle, Asymmetry tests for Bifurcating Auto-Regressive Processes with missing data. Stat. Probab. Lett. 82 (2012) 1439–1444. [CrossRef] [Google Scholar]
  14. B. De Saporta, A. Gégout-Petit and L. Marsalle, Random coefficients bifurcating autoregressive processes ESAIM: PS 18 (2014) 365–399. [CrossRef] [EDP Sciences] [Google Scholar]
  15. J.F. Delmas and L. Marsalle, Detection of cellular aging in Galton−Watson process. Stochastic Process. Appl. 120 (2010) 2495-2519 [Google Scholar]
  16. J.P. Dion and N.M. Yanev, Limit theorems and estimation theory for branching processes with increasing random number of ancestors. J. Appl. Probab. 34 (1997) 309–327. [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. [CrossRef] [Google Scholar]
  18. J. Guyon, A. Bize, G. Paul, E.J. Stewart, J.F. Delmas and F. Taddéi, Statistical study of cellular aging. Proc. of CEMRACS 2004. ESAIM: Proc. 14 (2005) 100–114. [Google Scholar]
  19. W. Hoeffding, Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58 (1963) 13–30. [CrossRef] [MathSciNet] [Google Scholar]
  20. R.B. Karp and Y. Zhang, Finite branching processes and AND/OR tree evaluation TR. International Computer Science Institute; 93-043, ICSI. Berkeley, Calif. (1994). [Google Scholar]
  21. C. McDiarmid, On the method of bounded differences. Electron. Comm. Probab. 11 (2006) 64–77. [MathSciNet] [Google Scholar]
  22. E.J. Stewart, R. Madden, G. Paul and F. Taddéi, Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Biol. 3 (2005) e45. [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.