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References

  • Afanasyev, V. I. On the survival probability of a subcritical branching process in a random environment. Dep. VINITI No. M1794--79 (1978) (in Russian).

  • Afanasyev, V. I.; Böinghoff, C.; Kersting, G.; Vatutin, V. A. Limit theorems for a weakly subcritical branching process in a random environment. to appear in J. Theoret. Probab. DOI: 10.1007/s10959-010-0331-6

  • 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 (2005k:60267)

  • Afanasyev, V. I.; Geiger, J.; Kersting, G.; Vatutin, V. A. Functional limit theorems for strongly subcritical branching processes in random environment. Stochastic Process. Appl. 115 (2005), no. 10, 1658--1676. MR2165338 (2006i:60119)

  • Böinghoff, C.; Hutzenthaler, M. Branching diffusions in random environment. (2011). ArXiv

  • Dufresne, Daniel. The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuar. J. 1990, no. 1-2, 39--79. MR1129194 (92i:62195)

  • Dyakonova, E. E.; Geiger, J.; Vatutin, V. A. On the survival probability and a functional limit theorem for branching processes in random environment. Markov Process. Related Fields 10 (2004), no. 2, 289--306. MR2082575 (2005i:60201)

  • 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 (88a:60130)

  • Jagers, Peter; Lagerås, Andreas N. General branching processes conditioned on extinction are still branching processes. Electron. Commun. Probab. 13 (2008), 540--547. MR2453547 (2010a:60289)

  • Karlin, Samuel; Taylor, Howard M. A second course in stochastic processes. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. xviii+542 pp. ISBN: 0-12-398650-8 MR0611513 (82j:60003)

  • Keiding, Niels Extinction and exponential growth in random environments. Theor. Population Biology 8 (1975), 49--63. DOI: 10.1016/0040-5809(75)90038-6

  • Kurtz, Thomas G. Diffusion approximations for branching processes. Branching processes (Conf., Saint Hippolyte, Que., 1976), pp. 269--292, Adv. Probab. Related Topics, 5, Dekker, New York, 1978. MR0517538 (80g:60089)

  • Vatutin, V. A. A limit theorem for an intermediate subcritical branching process in a random environment. (Russian) Teor. Veroyatnost. i Primenen. 48 (2003), no. 3, 453--465; translation in Theory Probab. Appl. 48 (2004), no. 3, 481--492 MR2141345 (2006a:60200)

  • Yor, Marc. Sur certaines fonctionnelles exponentielles du mouvement brownien réel. (French) [On some exponential functionals of real Brownian motion] J. Appl. Probab. 29 (1992), no. 1, 202--208. MR1147781 (93g:60179)

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