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References

  • Alsmeyer, G.; Iksanov, A.; Polotskiy, S.; Rosler, U. Exponential rate of $L_ p$-convergence of intrinsic martingales in supercritical branching random walks. Theory Stoch. Process. 15 (2009), no. 2, 1--18. MR2598524
  • Asmussen, Soren. Convergence rates for branching processes. Ann. Probability 4 (1976), no. 1, 139--146. MR0391286
  • Athreya, Krishna B.; Karlin, Samuel. On branching processes with random environments. I. Extinction probabilities. Ann. Math. Statist. 42 (1971), 1499--1520. MR0298780
  • Athreya, Krishna B.; Karlin, Samuel. Branching processes with random environments. II. Limit theorems. Ann. Math. Statist. 42 (1971), 1843--1858. MR0298781
  • Athreya, Krishna B.; Ney, Peter E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040
  • Afanasyev, V. I.; Geiger, J.; Kersting, G.; Vatutin, V. A. Criticality for branching processes in random environment. Ann. Probab. 33 (2005), no. 2, 645--673. MR2123206
  • Bansaye, V.; Berestycki, J. Large deviations for branching processes in random environment. Markov Process. Related Fields 15 (2009), no. 4, 493--524. MR2598126
  • Boinghoff, C.; Dyakonova, E. E.; Kersting, G.; Vatutin, V. A. Branching processes in random environment which extinct at a given moment. Markov Process. Related Fields 16 (2010), no. 2, 329--350. MR2666857
  • Chow, Yuan Shih; Teicher, Henry. Probability theory. Independence, interchangeability, martingales. Second edition. Springer Texts in Statistics. Springer-Verlag, New York, 1988. xviii+467 pp. ISBN: 0-387-96695-1 MR0953964
  • Grincevičjus, A. K. The continuity of the distribution of a certain sum of dependent variables that is connected with independent walks on lines. (Russian) Teor. Verojatnost. i Primenen. 19 (1974), 163--168. MR0345178
  • Guivarc'h, Yves; Liu, Quansheng. Proprietes asymptotiques des processus de branchement en environnement aleatoire. (French) [Asymptotic properties of branching processes in a random environment] C. R. Acad. Sci. Paris Ser. I Math. 332 (2001), no. 4, 339--344. MR1821473
  • Huang, Chunmao; Liu, Quansheng. Moments, moderate and large deviations for a branching process in a random environment. Stochastic Process. Appl. 122 (2012), no. 2, 522--545. MR2868929
  • Huang, Chunmao; Liu, Quansheng. Convergence rates for a branching process in a random environment. Markov Process. Related Fields 20 (2014), 265-286.
  • Jagers, Peter. Galton-Watson processes in varying environments. J. Appl. Probability 11 (1974), 174--178. MR0368197
  • Kozlov, M. V. On large deviations of branching processes in a random environment: a geometric distribution of the number of descendants. (Russian) Diskret. Mat. 18 (2006), no. 2, 29--47; translation in Discrete Math. Appl. 16 (2006), no. 2, 155--174 MR2283329
  • Liu, Quansheng. On generalized multiplicative cascades. Stochastic Process. Appl. 86 (2000), no. 2, 263--286. MR1741808
  • Liu, Quansheng. Local dimensions of the branching measure on a Galton-Watson tree. Ann. Inst. H. Poincare Probab. Statist. 37 (2001), no. 2, 195--222. MR1819123
  • Smith, Walter L.; Wilkinson, William E. On branching processes in random environments. Ann. Math. Statist. 40 1969 814--827. MR0246380
  • Tanny, David. A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means. Stochastic Process. Appl. 28 (1988), no. 1, 123--139. MR0936379


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