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References

  • S.V. Avery. Microbial cell individuality and the underlying sources of heterogeneity. phNat. Rev. Microbiol., 4:577--587, 2006.
  • Benjamini, Itai; Peres, Yuval. Markov chains indexed by trees. Ann. Probab. 22 (1994), no. 1, 219--243. MR1258875
  • Bercu, Bernard; de Saporta, Benoîte; Gégout-Petit, Anne. Asymptotic analysis for bifurcating autoregressive processes via a martingale approach. Electron. J. Probab. 14 (2009), no. 87, 2492--2526. MR2563249
  • Dawson, Donald A. Measure-valued Markov processes. École d'Été de Probabilités de Saint-Flour XXI—1991, 1--260, Lecture Notes in Math., 1541, Springer, Berlin, 1993. MR1242575
  • Delmas, Jean-François; Marsalle, Laurence. Detection of cellular aging in a Galton-Watson process. Stochastic Process. Appl. 120 (2010), no. 12, 2495--2519. MR2728175
  • de Saporta, Benoîte; Gégout-Petit, Anne; Marsalle, Laurence. Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. Electron. J. Stat. 5 (2011), 1313--1353. MR2842907
  • Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085
  • M.B. Elowitz, A.J. Levine, E.D. Siggia, and P. Swain. Stochastic gene expression in a single cell. phScience Signalling, 297:1183--1186, 2002.
  • Guyon, Julien. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann. Appl. Probab. 17 (2007), no. 5-6, 1538--1569. MR2358633
  • Jakubowski, Adam. On the Skorokhod topology. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 3, 263--285. MR0871083
  • Kallenberg, Olav. Foundations of modern probability. Second edition. Probability and its Applications (New York). Springer-Verlag, New York, 2002. xx+638 pp. ISBN: 0-387-95313-2 MR1876169
  • Liu, Wen; Wang, Liying. The Markov approximation of the random fields on Cayley trees and a class of small deviation theorems. Statist. Probab. Lett. 63 (2003), no. 2, 113--121. MR1986681
  • Liu, Wen; Yang, Weiguo. Some strong limit theorems for Markov chain fields on trees. Probab. Engrg. Inform. Sci. 18 (2004), no. 3, 411--422. MR2082475
  • H.H. McAdams and A. Arkin. It’s a noisy business! genetic regulation at the nanomolar scale. phTrends Genet., 15:65--69, 1999.
  • L. Pelkmans. Using cell-to-cell variability -- a new era in molecular biology. phScience, 336:425--426, 2012.
  • J.L. Spudich and D.E. Koshland. Non-genetic individuality: chance in the single cell. phNature, 262:467--471, 1976.
  • B. Snijder and L. Pelkmans. Origins of regulated cell-to-cell variability. phNat. Rev. Mol. Cell. Biol., 12:119--125, 2011.
  • Takacs, Christiane. On the fundamental matrix of finite state Markov chains, its eigensystem and its relation to hitting times. Math. Pannon. 17 (2006), no. 2, 183--193. MR2272894
  • Yang, Weiguo. Some limit properties for Markov chains indexed by a homogeneous tree. Statist. Probab. Lett. 65 (2003), no. 3, 241--250. MR2018036
  • Yang, Weiguo; Liu, Wen. Strong law of large numbers and Shannon-McMillan theorem for Markov chain fields on trees. IEEE Trans. Inform. Theory 48 (2002), no. 1, 313--318. MR1872187


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