Y. Benoist and J. Quint, Central limit theorem for linear groups, Ann. Probab, vol.44, issue.2, pp.1308-1340, 2016.

E. Bolthausen, On a functional central limit theorem for random walks conditioned to stay positive, Ann. Probability, vol.4, issue.3, pp.480-485, 1976.

, Products of random matrices with applications to Schrödinger operators, Progress in Probability and Statistics, vol.8, 1985.

D. Denisov and V. Wachtel, Random walks in cones, Ann. Probab, vol.43, issue.3, pp.992-1044, 2015.

N. Dunford and J. Schwarz, , 1958.

H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Statist, vol.31, pp.457-469, 1960.

I. Grama, E. L. Page, and M. Peigné, On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains, Colloq. Math, vol.134, issue.1, pp.1-55, 2014.

Y. Guivarc'h and A. Raugi, Frontì ere de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete, vol.69, issue.2, pp.187-242, 1985.

H. Hennion, Loi des grands nombres et perturbations pour des produits réductibles de matrices aléatoires indépendantes, Z. Wahrsch. Verw. Gebiete, vol.67, issue.3, pp.265-278, 1984.

H. Hennion, Limit theorems for products of positive random matrices, Ann. Probab, vol.25, issue.4, pp.1545-1587, 1997.

H. Hennion and L. Hervé, Stable laws and products of positive random matrices, J. Theoret. Probab, vol.21, issue.4, pp.966-981, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00360677

D. L. Iglehart, Functional central limit theorems for random walks conditioned to stay positive, Ann. Probab, vol.2, pp.608-619, 1974.

D. L. Iglehart, Random walks with negative drift conditioned to stay positive, J. Appl. Probability, vol.11, pp.742-751, 1974.

D. L. Iglehart, Conditioned limit theorems for random walks, 1975.

W. D. Kaigh, An invariance principle for random walk conditioned by a late return to zero, Ann. Probability, vol.4, issue.1, pp.115-121, 1976.

E. and L. Page, Théorèmes limites pour les produits de matrices aléatoires, Probability measures on groups, vol.928, pp.258-303, 1981.

L. Page, M. Peigné, and C. Pham, The survival probability of a critical multi-type branching process in i.i.d. random environment, Ann. Probab
URL : https://hal.archives-ouvertes.fr/hal-01705787

P. Levy, Théorie de l'addition des variables aléatoires, 1937.

M. Shimura, A class of conditional limit theorems related to ruin problem, Ann. Probab, vol.11, issue.1, pp.40-45, 1983.

V. I. Afanasyev, Limit theorem for the critical branching process in random environment, Discrete Math. Appl, vol.5, issue.1, p.1221669, 1993.

K. Athreya and S. Karlin, On branching process with random environment, I: extinction probabilities, Ann. Math. Statist, vol.42, issue.5, 1971.

K. Athreya and S. Karlin, On branching process with random environment, II: Limit theorem, Ann. Math. Statist, vol.42, issue.6, p.298781, 1971.

V. Bansaye and J. Berestycki, Large deviations for Branching Processes in Random Environment, Markov Process. Related Fields, vol.15, pp.493-524, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00453402

. Ph, J. Bougerol, and . Lacroix, Products of Random Matrices with Applications to Schrödinger Operators, Birkhäuser, p.886674, 1985.

E. E. Dyakonova, Asymptotics behaviour of the probability of non-extinction for a multi-type branching process in a random environment, Discrete Math. Appl, vol.9, issue.2, pp.119-136, 1999.

E. E. Dyakonova, J. Geiger, and V. A. Vatutin, On the survival probability and a functional limit theorem for branching processes in random environment, Markov Process. related Fields, vol.10, p.2082575, 2004.

E. E. Dyakonova and V. A. Vatutin, Multitype branching processes in random environment: survival probability for the critical case, Theory Probab. Appl, vol.62, issue.4, pp.506-521, 2018.

H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Statist, vol.31, pp.457-469, 1960.

J. Geiger and G. Kersting, The survival probability of a critical branching process in random environment, Theory. Probab. Appl, vol.45, issue.3, pp.518-526, 2002.

J. Geiger, G. Kersting, and V. A. Vatutin, Limit theorems for subcritical branching processes in random environment, Ann. de l'I.H.P. Probab. et Statist, vol.39, issue.4, 2003.

I. Grama, E. L. Page, and M. Peigné, On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains, Colloquium Mathematicum, vol.134, pp.1-55, 2014.

I. Grama, E. L. Page, and M. Peigné, Conditional limit theorems for products of random matrices, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01270418

Y. Guivarc'h and J. Hardy, Théorèmes limites pour une classe de cha??nescha??nes de Markov et applications aux difféomorphismes d, Anosov. Ann. Inst. H. Poincaré Probab. Statist, vol.24, issue.1, pp.73-98, 1988.

Y. Guivarc'h, E. L. Page, and Q. Liu, Normalisation d'un processus de branchement critique dans un environnement aléatoire, C. R. Acad. Sci. Paris Sér. I Math, vol.337, pp.603-608, 2003.

Y. Guivarc'h and Q. Liu, Asymptotic properties of branching processes in a random environment, C. R. Acad. Sci. Paris Sér. I Math, vol.332, p.1821473, 2001.

H. Hennion, Limit theorems for products of positive random matrices, Ann. Probab, vol.25, issue.4, pp.1545-1587, 1997.

N. Kaplan, Some results about multidimensional branching processes with random environments, Ann. Probab, vol.0378127, issue.2, pp.441-455, 1974.

M. V. Kozlov, On the asymptotic bahaviour of the probability of non-extinction for critical branching processes in a random environment, Theor. of. Probab. and its Appl, vol.XXI, issue.4, p.428492, 1976.

E. and L. Page, Théorèmes limites pour les produits de matrices aléatoires, Lecture Notes, vol.928, p.669072, 1982.

T. D. Pham, Conditioned limit theorems for products of positive random matrices, ALEA, Lat. Am. J. Probab. Math. Stat, vol.15, pp.67-100, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01959053

W. L. Smith and W. Wilkinson, On branching processes in random environment, Adv. Math. Statist, vol.40, issue.3, p.246380, 1969.

A. M. Zubkov, Inequalities for the distribution of the numbers of simultaneous events, Survey of Appl. and Industry math. Ser. Probab. and Stat, vol.1, pp.638-666, 1994.

F. Vannes,

E. ,

F. Tours, E-mail: Marc.Peigne@lmpt.univ-tours.fr E-mail: Da-Cam

. Bibliographie-[abraham, R. Abraham, and J. P. Et-delmas, An introduction on galton-watson trees and their local limits, ESAIM : Proceedings and Surveys, 7. ESAIM : Proceedings and Surveys, 2016.

V. I. Afanasyev, A limit theorem for a critical branching process in a random environment, Diskret. Mat, vol.5, issue.1, pp.45-58, 1993.

. Afanasyev, Criticality for branching processes in random environment, Ann. Probab, vol.33, issue.2, pp.645-673, 2005.

K. B. Athreya-et-karlin-;-athreya and S. Et-karlin, Branching processes with random environments. II. Limit theorems, Ann. Math. Statist, vol.42, pp.1843-1858, 1971.

K. B. Athreya-et-karlin-;-athreya and S. Et-karlin, On branching processes with random environments. I. Extinction probabilities, Ann. Math. Statist, vol.42, pp.1499-1520, 1971.

K. B. Athreya and P. E. Et-ney, Branching processes, Die Grundlehren der mathematischen Wissenschaften, 0196.

[. Babillot, The random difference equation X n = A n X n?1 + B n in the critical case, Ann. Probab, vol.25, issue.1, pp.478-493, 1997.

. Bansaye, V. Berestycki-;-bansaye, and J. Berestycki, Large deviations for branching processes in random environment, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00453402

Y. Benoist and J. Quint, Central limit theorem for linear groups, Ann. Probab, vol.44, issue.2, pp.1308-1340, 2016.

P. Billingsley, Convergence of probability measures, 1968.

E. Bolthausen, On a functional central limit theorem for random walks conditioned to stay positive, Ann. Probability, vol.4, issue.3, pp.480-485, 1976.

P. Bougerol, J. Lacroix, and S. Brofferio, Products of random matrices with applications to Schrödinger operators, Ann. Inst. H. Poincaré Probab. Statist, vol.8, issue.3, pp.371-384, 1985.

Y. S. Chow and H. Teicher, Probability theory : independence, interchangeability, martingales, 2012.

B. Church and J. D. , On infinite composition products of probability generating functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, vol.19, pp.243-256, 1971.

H. Cohn, On the growth of the multitype supercritical branching process in a random environment, Ann. Probab, vol.17, issue.3, pp.1118-1123, 1989.

E. E. Dyakonova, The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment, Diskret. Mat, vol.11, issue.1, pp.113-128, 1999.

D. Denisov and V. Wachtel, Random walks in cones, Ann. Probab, vol.43, issue.3, pp.992-1044, 2015.

[. Dolgopyat, , 2017.

, Multi-type branching processes with time-dependent branching rates

[. Dyakonova, On the survival probability and a functional limit theorem for branching processes in random environment, Markov Process. Related Fields, vol.10, issue.2, pp.289-306, 2004.

W. Feller, An introduction to probability theory and its applications, 1968.

H. Furstenberg and H. Et-kesten, Products of random matrices, Ann. Math. Statist, vol.31, pp.457-469, 1960.

J. Geiger and G. Kersting, The survival probability of a critical branching process in random environment, Teor. Veroyatnost. i Primenen, vol.45, issue.3, pp.607-615, 2000.

[. Geiger, Limit theorems for subcritical branching processes in random environment, Ann. Inst. H. Poincaré Probab. Statist, vol.39, issue.4, pp.593-620, 2003.

[. Grama, On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains, Colloq. Math, vol.134, issue.1, pp.1-55, 2014.

[. Grama, Conditioned limit theorems for products of random matrices, Probab. Theory Related Fields, vol.168, issue.3-4, pp.601-639, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01449023

A. K. Grincevi?jus, A central limit theorem for the group of linear transformations of the line, Dokl. Akad. Nauk SSSR, vol.219, pp.23-26, 1974.

Y. Guivarc'h-et-raugi-;-guivarc'h and A. Et-raugi, Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete, vol.69, issue.2, pp.187-242, 1985.

T. E. Harris, Loi des grands nombres et perturbations pour des produits réductibles de matrices aléatoires indépendantes, Z. Wahrsch. Verw. Gebiete, vol.67, issue.3, pp.265-278, 1963.

H. Hennion, Limit theorems for products of positive random matrices, Ann. Probab, vol.25, issue.4, pp.1545-1587, 1997.

. Bibliographie-[hennion, H. Hervé-;-hennion, and L. Hervé, Stable laws and products of positive random matrices, J. Theoret. Probab, vol.21, issue.4, pp.966-981, 2008.

D. L. Iglehart, Functional central limit theorems for random walks conditioned to stay positive, Ann. Probability, vol.2, pp.608-619, 1974.

D. L. Iglehart, Random walks with negative drift conditioned to stay positive, J. Appl. Probability, vol.11, pp.742-751, 1974.

D. L. Iglehart, Conditioned limit theorems for random walks, pp.167-194, 1975.

P. Jagers and W. D. Kaigh, An invariance principle for random walk conditioned by a late return to zero, Ann. Probability, vol.1, issue.1, pp.115-121, 1976.

N. Kaplan, Some results about multidimensional branching processes with random environments, Ann. Probability, vol.2, pp.441-455, 1974.

G. Kersting, A unifying approach to branching processes in varying environments, 2017.

H. Kesten and B. P. Stigum, A limit theorem for multidimensional Galton-Watson processes, Ann. Math. Statist, vol.37, pp.1211-1223, 1966.

A. N. Kolmogorov, Zur lösung einer biologishen aufgabe, Iz. NII. Mathem. Mekh. Tomskogo Univ, vol.2, pp.1-6, 1938.

M. V. Kozlov, On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment, Theory of Probability & Its Applications, vol.21, pp.791-804, 1977.

R. Lauvergnat, Théorèmes limites pour des marches aléatoires markoviennes conditionnées à rester positives, 2017.

E. Page-;-le-page, Théorèmes limites pour les produits de matrices aléatoires, Probability measures on groups, vol.928, pp.258-303, 1981.

[. Page, E. Peigné, and M. , A local limit theorem on the semi-direct product of R * + and R d, Ann. Inst. H. Poincaré Probab. Statist, vol.33, issue.2, pp.223-252, 1997.

[. Page, The survival probability of a critical multi-type branching process in i.i.d. random environment, Ann. Probab, vol.46, issue.5, pp.2946-2972, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01705787

T. Lindvall, Lectures on the coupling method, Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, 1992.

C. J. Mode, Multitype branching processes, Theory and applications. Modern Analytic and Computational Methods in Science and Mathematics, issue.34, 1971.

R. E. Paley and N. Wiener, Fourier transforms in the complex domain, vol.19, 1987.

B. Pham and T. D. , Conditioned limit theorems for products of positive random matrices, ALEA Lat. Am. J. Probab. Math. Stat, vol.15, issue.1, pp.67-100, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01959053

W. L. Smith and W. E. Et-wilkinson, On branching processes in random environments, Ann. Math. Statist, vol.40, pp.814-827, 1969.

F. Spitzer, Principles of random walk, Graduate Texts in Mathematics, vol.34, 1976.

V. A. Vatutin and E. E. Dyakonova, Multitype branching processes in a random environment : nonextinction probability in the critical case, Teor. Veroyatn. Primen, vol.62, issue.4, pp.634-653, 2017.