The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • 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, Vincent. Proliferating parasites in dividing cells: Kimmel's branching model revisited. Ann. Appl. Probab. 18 (2008), no. 3, 967--996. MR2418235
  • Bansaye, Vincent. Surviving particles for subcritical branching processes in random environment. Stochastic Process. Appl. 119 (2009), no. 8, 2436--2464. MR2532207
  • Vincent Bansaye and Florian Simatos. On the scaling limits of Galton-Watson processes in varying environment. arXiv:1112.2547., 2013.
  • Bansaye, Vincent; Tran, Viet Chi. Branching Feller diffusion for cell division with parasite infection. ALEA Lat. Am. J. Probab. Math. Stat. 8 (2011), 95--127. MR2754402
  • Bertoin, Jean; Le Gall, Jean-François. The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Probab. Theory Related Fields 117 (2000), no. 2, 249--266. MR1771663
  • Bertoin, Jean; Yor, Marc. Exponential functionals of Lévy processes. Probab. Surv. 2 (2005), 191--212. MR2178044
  • Bingham, N. H. Continuous branching processes and spectral positivity. Stochastic Processes Appl. 4 (1976), no. 3, 217--242. MR0410961
  • Böinghoff, C.; Hutzenthaler, M. Branching diffusions in random environment. Markov Process. Related Fields 18 (2012), no. 2, 269--310. MR2985138
  • Brockwell, P. J. The extinction time of a birth, death and catastrophe process and of a related diffusion model. Adv. in Appl. Probab. 17 (1985), no. 1, 42--52. MR0778592
  • Philippe Carmona, Frédérique Petit, and Marc Yor. On the distribution and asymptotic results for exponential functionals of Lévy processes. In Exponential functionals and principal values related to Brownian motion, Bibl. Rev. Mat. Iberoamericana, pages 73--130. Rev. Mat. Iberoamericana, Madrid, 1997.
  • Etienne Danchin, Luc-Alain Giraldeau, and Frank Cézilly. Behavioural Ecology: An Evolutionary Perspective on Behaviour. Oxford University Press, 2008.
  • Doney, R. A.; Maller, R. A. Stability and attraction to normality for Lévy processes at zero and at infinity. J. Theoret. Probab. 15 (2002), no. 3, 751--792. MR1922446
  • Dynkin, E. B. Branching particle systems and superprocesses. Ann. Probab. 19 (1991), no. 3, 1157--1194. MR1112411
  • 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
  • Fu, Zongfei; Li, Zenghu. Stochastic equations of non-negative processes with jumps. Stochastic Process. Appl. 120 (2010), no. 3, 306--330. MR2584896
  • Geiger, J.; Kersting, G. The survival probability of a critical branching process in random environment. Teor. Veroyatnost. i Primenen. 45 (2000), no. 3, 607--615; translation in Theory Probab. Appl. 45 (2002), no. 3, 518--526 MR1967796
  • Geiger, Jochen; Kersting, Götz; Vatutin, Vladimir A. Limit theorems for subcritical branching processes in random environment. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 4, 593--620. MR1983172
  • Grey, D. R. Asymptotic behaviour of continuous time, continuous state-space branching processes. J. Appl. Probability 11 (1974), 669--677. MR0408016
  • Grimvall, Anders. On the convergence of sequences of branching processes. Ann. Probability 2 (1974), 1027--1045. MR0362529
  • Guivarc'h, Yves; Liu, Quansheng. Propriétés asymptotiques des processus de branchement en environnement aléatoire. (French) [Asymptotic properties of branching processes in a random environment] C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 4, 339--344. MR1821473
  • Hirano, Katsuhiro. Determination of the limiting coefficient for exponential functionals of random walks with positive drift. J. Math. Sci. Univ. Tokyo 5 (1998), no. 2, 299--332. MR1633937
  • Hutzenthaler, Martin. Supercritical branching diffusions in random environment. Electron. Commun. Probab. 16 (2011), 781--791. MR2868599
  • Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes. Second edition. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. xvi+555 pp. ISBN: 0-444-87378-3 MR1011252
  • Jiřina, Miloslav. Stochastic branching processes with continuous state space. Czechoslovak Math. J. 8 (83) 1958 292--313. MR0101554
  • Kozlov, M. V. The asymptotic behavior of the probability of non-extinction of critical branching processes in a random environment. (Russian) Teor. Verojatnost. i Primenen. 21 (1976), no. 4, 813--825. MR0428492
  • Kyprianou, Andreas E. Introductory lectures on fluctuations of Lévy processes with applications. Universitext. Springer-Verlag, Berlin, 2006. xiv+373 pp. ISBN: 978-3-540-31342-7; 3-540-31342-7 MR2250061
  • Lambert, Amaury. Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct. Electron. J. Probab. 12 (2007), no. 14, 420--446. MR2299923
  • Lambert, Amaury. Population dynamics and random genealogies. Stoch. Models 24 (2008), suppl. 1, 45--163. MR2466449
  • Lamperti, John. Continuous state branching processes. Bull. Amer. Math. Soc. 73 1967 382--386. MR0208685
  • Lamperti, John. The limit of a sequence of branching processes. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 1967 271--288. MR0217893
  • R. Lande. Risks of population extinction from demographic and environmental stochasticity and random catastrophes. American Naturalist, pages 911--927, 1993.
  • Russell Lande, Steinar Engen, and Bernt-Erik Saether. Stochastic Population Dynamics in Ecology and Conservation. Oxford University Press, 2003.
  • Le Page, Émile; Peigné, Marc. A local limit theorem on the semi-direct product of ${\bf R}^ {*+}$ and ${\bf R}^ d$. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), no. 2, 223--252. MR1443957
  • Nicolas~O Rode, Eva~JP Lievens, Elodie Flaven, Adeline Segard, Roula Jabbour-Zahab, Marta~I Sanchez, and Thomas Lenormand. Why join groups? Lessons from parasite-manipulated artemia. Ecology letters, 2013.
  • Silverstein, M. L. A new approach to local times. J. Math. Mech. 17 1967/1968 1023--1054. MR0226734
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.