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References

  • Albeverio, S.; Bogachev, L. V.; Molchanov, S. A.; Yarovaya, E. B. Annealed moment Lyapunov exponents for a branching random walk in a homogeneous random branching environment. Markov Process. Related Fields 6 (2000), no. 4, 473--516. MR1805091
  • Bartsch, C.; Gantert, N.; Kochler, M. Survival and growth of a branching random walk in random environment. Markov Process. Related Fields 15 (2009), no. 4, 525--548. MR2598127
  • Benjamini, Itai; Peres, Yuval. Markov chains indexed by trees. Ann. Probab. 22 (1994), no. 1, 219--243. MR1258875
  • Birkner, Matthias; Geiger, Jochen; Kersting, Götz. Branching processes in random environment—a view on critical and subcritical cases. Interacting stochastic systems, 269--291, Springer, Berlin, 2005. MR2118578
  • Carmona, René A.; Molchanov, S. A. Parabolic Anderson problem and intermittency. Mem. Amer. Math. Soc. 108 (1994), no. 518, viii+125 pp. MR1185878
  • Comets, F.; Menshikov, M. V.; Popov, S. Yu. One-dimensional branching random walk in a random environment: a classification. I Brazilian School in Probability (Rio de Janeiro, 1997). Markov Process. Related Fields 4 (1998), no. 4, 465--477. MR1677053
  • Comets, Francis; Popov, Serguei. Shape and local growth for multidimensional branching random walks in random environment. ALEA Lat. Am. J. Probab. Math. Stat. 3 (2007), 273--299. MR2365644
  • Comets, Francis; Yoshida, Nobuo. Branching random walks in space-time random environment: survival probability, global and local growth rates. J. Theoret. Probab. 24 (2011), no. 3, 657--687. MR2822477
  • Donsker, M. D. and Varadhan, S. R. S.: Asymptotic evaluation of certain Markov process expectations for large time, I--IV, ph Comm. Pure Appl. Math. 28, (1975), 1--47, 279--301; 29, (1976), 389--461; 36, 183--212 (1983). MR0386024, MR0428471, MR0690656
  • Gantert, Nina; Müller, Sebastian; Popov, Serguei; Vachkovskaia, Marina. Survival of branching random walks in random environment. J. Theoret. Probab. 23 (2010), no. 4, 1002--1014. MR2735734
  • Gertner, Jurgen. On large deviations from an invariant measure. (Russian) Teor. Verojatnost. i Primenen. 22 (1977), no. 1, 27--42. MR0471040
  • Gärtner, Jürgen; König, Wolfgang. The parabolic Anderson model. Interacting stochastic systems, 153--179, Springer, Berlin, 2005. MR2118574
  • Gärtner, J.; Molchanov, S. A. Parabolic problems for the Anderson model. I. Intermittency and related topics. Comm. Math. Phys. 132 (1990), no. 3, 613--655. MR1069840
  • Gärtner, J.; Molchanov, S. A. Parabolic problems for the Anderson model. II. Second-order asymptotics and structure of high peaks. Probab. Theory Related Fields 111 (1998), no. 1, 17--55. MR1626766
  • Harris, S. and Roberts, M. I.: The many-to-few lemma and multiple spines, ARXIV1106.4761
  • van der Hofstad, Remco; König, Wolfgang; Mörters, Peter. The universality classes in the parabolic Anderson model. Comm. Math. Phys. 267 (2006), no. 2, 307--353. MR2249772
  • Machado, F. P.; Popov, S. Yu. One-dimensional branching random walks in a Markovian random environment. J. Appl. Probab. 37 (2000), no. 4, 1157--1163. MR1808881
  • Machado, F. P.; Popov, S. Yu. Branching random walk in random environment on trees. Stochastic Process. Appl. 106 (2003), no. 1, 95--106. MR1983045
  • Molchanov, S. Lectures on random media. Lectures on probability theory (Saint-Flour, 1992), 242--411, Lecture Notes in Math., 1581, Springer, Berlin, 1994. MR1307415
  • Molchanov, S. Reaction-diffusion equations in the random media: localization and intermittency. Nonlinear stochastic PDEs (Minneapolis, MN, 1994), 81--109, IMA Vol. Math. Appl., 77, Springer, New York, 1996. MR1395894
  • Müller, S. Recurrence and transience for branching random walks in an I.I.D. random environment. Markov Process. Related Fields 14 (2008), no. 1, 115--130. MR2433298
  • Yoshida, Nobuo. Central limit theorem for branching random walks in random environment. Ann. Appl. Probab. 18 (2008), no. 4, 1619--1635. MR2434183


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