[1]
Afanasyev, V. I. (1993). A limit theorem for a critical branching process in random environment. Diskret. Mat.
5, 45–58 (in Russian).
[2]
Afanasyev, V. I. (1997). A new theorem for a critical branching process in random environment. Discrete Math. Appl.
7, 497–513.
[3]
Afanasyev, V. I. (1999). On the maximum of a critical branching process in a random environment. Discrete Math. Appl.
9, 267–284.
[4]
Afanasyev, V. I. (1999). On the time of reaching a fixed level by a critical branching process in a random environment. Discrete Math. Appl.
9, 627–643.
[5]
Afanasyev, V. I. (2001). A functional limit theorem for a critical branching process in a random environment. Discrete Math. Appl.
11, 587–606.
[6]
Afanasyev, V. I., Böinghoff, C., Kersting, G. and Vatutin, V. A. (2012). Limit theorems for weakly subcritical branching processes in random environment. J. Theoret. Prob.
25, 703–732.
[7]
Afanasyev, V. I., Böinghoff, C., Kersting, G. and Vatutin, V. A. (2014). Conditional limit theorems for intermediately subcritical branching processes in random environment. Ann. Inst. H. Poincaré Prob. Statist.
50, 602–627.
[8]
Afanasyev, V. I., Geiger, J., Kersting, G. and Vatutin, V. A. (2005). Criticality for branching processes in random environment. Ann. Prob.
33, 645–673.
[9]
Afanasyev, V. I., Geiger, J., Kersting, G. and Vatutin, V. A. (2005). Functional limit theorems for strongly subcritical branching processes in random environment. Stoch. Process Appl.
115, 1658–1676.
[10]
Bertoin, J. and Doney, R. A. (1994). On conditioning a random walk to stay nonnegative. Ann. Prob.
22, 2152–2167.
[11]
Billingsley, P. (1999). Convergence of Probability Measures, 2nd edn. John Willey, New York.
[12]
Böinghoff, C., Dyakonova, E. E., Kersting, G. and Vatutin, V. A. (2010). Branching processes in random environment which extinct at a given moment. Markov Process. Relat. Fields
16, 329–350.
[13]
Caravenna, F. and Chaumont, L. (2008). Invariance principles for random walks conditioned to stay positive. Ann. Inst. H. Poincaré Prob. Statist.
44, 170–190.
[14]
Chaumont, L. (1996). Conditionings and path decompositions for Lévy processes. Stoch. Process. Appl.
64, 39–54.
[15]
Chaumont, L. (1997). Excursion normalisée, méandre at pont pour les processus de Lévy stables. Bull. Sci. Math.
121, 377–403.
[16]
Doney, R. A. (2012). Local behavior of first passage probabilities. Prob. Theory Relat. Fields
152, 559–588.
[17]
Dyakonova, E. E., Geiger, J. and Vatutin, V. A. (2004). On the survival probability and a functional limit theorem for branching processes in random environment. Markov Process. Relat. Fields
10, 289–306.
[18]
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. John Wiley, New York.
[19]
Geiger, J. and Kersting, G. (2002). The survival probability of a critical branching process in random environment. Theory Prob. Appl.
45, 518–526.
[20]
Kozlov, M. V. (1976). On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment. Theory Prob. Appl.
21, 791–804.
[21]
Kozlov, M. V. (1995). A conditional function limit theorem for a critical branching process in a random environment. Dokl. Akad. Nauk
344, 12–15 (in Russian).
[22]
Seneta, E. (1976). Regularly Varying Functions (Lecture Notes Math. 508). Springer, Berlin.
[23]
Vatutin, V. A. (2003). Reduced branching processes in a random environment: the critical case. Theory Prob. Appl.
47, 99–113.
[24]
Vatutin, V. A. (2016). Subcritical branching processes in random environment. In Branching Processes and Their Applications (Lecture Notes Statist. 219), eds I. M. del Puerto et al., Springer, Cham, pp. 97–115.
[25]
Vatutin, V. A. and Dyakonova, E. E. (2004). Galton–Watson branching processes in a random environment. I. Limit theorems. Theory Prob. Appl.
48, 314–336.
[26]
Vatutin, V. and Liu, Q. (2015). Limit theorems for decomposable branching processes in a random environment. J. Appl. Prob.
52, 877–.
[27]
Vatutin, V. A. and Wachtel, V. (2009). Local probabilities for random walks conditioned to stay positive. Prob. Theory Relat. Fields
143, 177–217.
[28]
Vatutin, V. A., Dyakonova, E. E. and Sagitov, S. (2013). Evolution of branching processes in a random environment. Proc. Steklov Inst. Math.
282, 220–242.
[29]
Zolotarev, V. M. (1957). Mellin–Stieltjes transform in probability theory. Theory Prob. Appl.
2, 433–460.
