Free Access
Issue
ESAIM: PS
Volume 23, 2019
Page(s) 823 - 840
DOI https://doi.org/10.1051/ps/2019006
Published online 24 December 2019
  1. L. Addario-Berry and B. Reed, Minima in branching random walks. Ann. Probab. 37 (2009) 1044–1079. [Google Scholar]
  2. V.I. Afanasyev, On the maximum of a subcritical branching process in a random environment. Stochastic Process. Appl. 93 (2001) 87–107. [CrossRef] [Google Scholar]
  3. V.I. Afanasyev, High level subcritical branching processes in a random environment. Proc. Steklov Inst. Math. 282 (2013) 4–14. [CrossRef] [Google Scholar]
  4. E. Aïdékon, Convergence in law of the minimum of a branching random walk. Ann. Probab. 41 (2013) 1362–1426. [Google Scholar]
  5. R. Bahadur and R. Rango, Rao On deviations of the sample mean. Ann. Math. Statist. 31 (1960) 1015–1027. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.D. Biggins, The first- and last-birth problems for a multitype age-dependent branching process. Adv. Appl. Probab. 8 (1976) 446–459. [Google Scholar]
  7. D. Buraczewski, J.F. Collamore, E. Damek and J. Zienkiewicz, Large deviation estimates for exceedance times of perpetuity sequences and their dual processes. Ann. Probab. 44 (2016) 3688–3739. [Google Scholar]
  8. D. Buraczewski, E. Damek and J. Zienkiewicz, Pointwise estimates for first passage times of perpetuity sequences. Stochastic Process. Appl. 128 (2018) 2923–2951. [CrossRef] [Google Scholar]
  9. D. Buraczewski, E. Damek and J. Zienkiewicz, Precise tail asymptotics of fixed points of the smoothing transform with general weights. Bernoulli 21 (2015) 489–504. [CrossRef] [Google Scholar]
  10. D. Buraczewski and P. Dyszewski, Large deviation estimates for branching process in random environment. Electron. J. Probab. 23 (2018) 26 pp. [Google Scholar]
  11. D. Buraczewski and M. Maślanka, Precise large deviations for the first passage time of random walk with negative drift. Proc. Amer. Math. Soc. 147 (2019) 4045–4054. [CrossRef] [Google Scholar]
  12. X. Chen and H. He, On large deviation probabilities for empirical distribution of branching random walks: Schröder case and Böttcher case. Preprint arXiv:1704.03776 (2017). [Google Scholar]
  13. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. Jones and Bartlett, Boston (1993). [Google Scholar]
  14. N. Gantert and T. Höfelsauer, Large deviations for the maximum of a branching random walk. Electron. Commun. Probab. 23 (2018) 34. [CrossRef] [Google Scholar]
  15. J.M. Hammersley, Postulates for subadditive processes. Ann. Probab. 2 (1974) 652–680. [Google Scholar]
  16. T. Höglund, An Asymptotic Expression for the Probability of Ruin within Finite Time. Ann. Probab. 18 (1990) 378–389. [Google Scholar]
  17. Y. Hu and Z. Shi, Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees. Ann. Probab. 37 (2009) 742–789. [Google Scholar]
  18. P. Jelenkovic and M. Olvera-Cravioto, Maximums on trees. Stochastic Process. Appl. 125 (2015) 217–232. [CrossRef] [Google Scholar]
  19. J.F.C. Kingman, The first birth problem for an age-dependent branching process. Ann. Probab. 3 (1975) 790–801. [Google Scholar]
  20. S. Lalley, Limit theorems for first-passage times in linear and nonlinear renewal theory. Adv. Appl. Probab. 16 (1984) 766–803. [Google Scholar]
  21. V. Petrov, On the probabilities of large deviations for sums of independent random variables. Theory Probab. Appl. 10 (1965) 287–298. [CrossRef] [Google Scholar]
  22. A. Rouault, Precise estimates of presence probabilities in the branching random walk. Stochastic Process. Appl. 44 (1993) 27–39. [CrossRef] [Google Scholar]
  23. Z. Shi, Branching random walks. Springer (2015). [CrossRef] [Google Scholar]
  24. B. von Bahr Ruin probabilities expressed in terms of ladder height distributions. Scand. Actuar. J. 1974 (1974) 190–204. [Google Scholar]

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