Free Access
Volume 23, 2019
Page(s) 823 - 840
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]

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.