V. I. Afanasyev, Limit theorems for a moderately subcritical branching process in a random environment, Discrete Mathematics and Applications, vol.8, issue.1, pp.35-52, 2009.
DOI : 10.1515/dma.1998.8.1.35

A. Agresti, Bounds on the extinction time distribution of a branching process, Advances in Applied Probability, vol.6, issue.02, pp.322-335, 1974.
DOI : 10.1017/S0021900200114081

K. B. Athreya and S. Karlin, Branching processes with random environments II: Limit theorems. The Annals of Mathematical Statistics, pp.1843-1858, 1971.
DOI : 10.1214/aoms/1177693051
URL : http://doi.org/10.1214/aoms/1177693051

K. B. Athreya and S. Karlin, Branching processes with random environments, Bulletin of the American Mathematical Society, vol.76, issue.4, pp.1499-1520, 1971.
DOI : 10.1090/S0002-9904-1970-12589-7
URL : http://www.ams.org/bull/1970-76-04/S0002-9904-1970-12589-7/S0002-9904-1970-12589-7.pdf

K. B. Athreya and P. E. Ney, Branching Processes, pp.978-981, 1972.

J. Bertoin and R. A. Doney, On conditioning a random walk to stay nonnegative. The Annals of Probability, pp.2152-2167, 1994.

N. H. Bingham, Limit theorems in fluctuation theory, Advances in Applied Probability, vol.2, issue.03, pp.554-569, 1973.
DOI : 10.1137/1116067

E. Bolthausen, On a functional central limit theorem for random walks conditioned to stay positive. The Annals of Probability, pp.480-485, 1976.

A. A. Borovkov, On the Asymptotic Behavior of the Distributions of First-Passage Times, I, Mathematical Notes, vol.75, issue.1/2, pp.23-37, 2004.
DOI : 10.1023/B:MATN.0000015019.37128.cb

A. A. Borovkov, On the Asymptotic Behavior of Distributions of First-Passage Times, II, Mathematical Notes, vol.75, issue.3/4, pp.322-330, 2004.
DOI : 10.1023/B:MATN.0000023311.52852.25

D. Buraczewski, E. Damek, and Y. , Guivarc'h. Convergence to stable laws for a class of multidimensional stochastic recursions. Probability Theory and Related Fields, pp.3-4333, 2009.

F. Caravenna, A local limit theorem for random walks conditioned to stay positive. Probability Theory and Related Fields, pp.508-530, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00003180

F. M. Dekking, On the survival probability of a branching process in a finite state i.i.d. environment, Stochastic Processes and their Applications, pp.151-157, 1987.
DOI : 10.1016/0304-4149(87)90011-1

A. Dembo, J. Ding, and F. Gao, Persistence of iterated partial sums. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, pp.873-884, 2013.

D. Denisov, D. Korshunov, and V. Wachtel, Harmonic functions and stationary distributions for asymptotically homogeneous transition kernels on Z +

D. Denisov, V. Vatutin, and V. Wachtel, Local probabilities for random walks with negative drift conditioned to stay nonnegative, Electronic Journal of Probability, vol.19, issue.0, pp.1-17, 2014.
DOI : 10.1214/EJP.v19-3426

D. Denisov and V. Wachtel, Conditional Limit Theorems for Ordered Random Walks, Electronic Journal of Probability, vol.15, issue.0, pp.292-322, 2010.
DOI : 10.1214/EJP.v15-752
URL : http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/include/getdocc646.pdf?article%3D2067%26id%3D5471%26mode%3Dpdf

D. Denisov and V. Wachtel, Exit times for integrated random walks. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, pp.167-193, 2015.
DOI : 10.1214/13-aihp577
URL : http://arxiv.org/pdf/1207.2270.pdf

D. Denisov and V. Wachtel, Random walks in cones. The Annals of Probability, pp.992-1044, 2015.

R. A. Doney, Conditional limit theorems for asymptotically stable random walks, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.11, issue.3, pp.351-360, 1985.
DOI : 10.1007/BF00534868

R. A. Doney, On the asymptotic behaviour of first passage times for transient random walk. Probability Theory and Related Fields, pp.239-246, 1989.

J. C. D-'souza and B. M. Hambly, On the Survival Probability of a Branching Process in a Random Environment, Advances in Applied Probability, vol.27, issue.01, pp.38-55, 1997.
DOI : 10.1016/0304-4149(94)00048-X

J. Duraj, Random walks in cones: The case of nonzero drift, Stochastic Processes and their Applications, pp.1503-1518, 2014.
DOI : 10.1016/j.spa.2013.12.003

J. Duraj and V. Wachtel, Invariance principles for random walks in cones, 2015.

P. Eichelsbacher and W. König, Ordered Random Walks, Electronic Journal of Probability, vol.13, issue.0, pp.1307-1336, 2008.
DOI : 10.1214/EJP.v13-539

D. J. Emery, Limiting behaviour of the distributions of the maxima of partial sums of certain random walks, Journal of Applied Probability, vol.2, issue.03, pp.572-579, 1972.
DOI : 10.1007/BF02591508

W. Feller, An Introduction to Probability Theory and Its Applications, 1971.

Z. Gao, Y. Guivarc-'h, and É. L. Page, Stable laws and spectral gap properties for affine random walks. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, pp.319-348, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01124425

R. Garbit, A central limit theorem for two-dimensional random walks in a cone, Bulletin de la Société mathématique de France, vol.139, issue.2, pp.271-286, 2011.
DOI : 10.24033/bsmf.2608
URL : https://hal.archives-ouvertes.fr/hal-00435499

J. Geiger and G. Kersting, The survival probability of a critical branching process in a random environment, Theory of Probability & Its Applications, pp.517-525, 2001.

J. Geiger, G. Kersting, and V. A. Vatutin, Limit theorems for subcritical branching processes in random environment, Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, pp.593-620, 2003.

B. V. Gnedenko, On a local limit theorem of the theory of probability, Uspekhi Matematicheskikh Nauk, pp.187-194, 1948.

M. I. Gordin, Central limit theorem for stationary processes, Doklady Akademii Nauk SSSR, vol.188, issue.4, pp.739-741, 1969.

I. Grama, R. Lauvergnat, and É. L. Page, Limit theorems for affine Markov walks conditioned to stay positive. Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, in press, 2016.
DOI : 10.1214/16-aihp814
URL : https://hal.archives-ouvertes.fr/hal-01264999

I. Grama, R. Lauvergnat, and É. L. Page, Conditioned local limit theorems for random walks defined on finite Markov chains, p.2017

I. Grama, R. Lauvergnat, and É. L. Page, Limit theorems for Markov walks conditioned to stay positive under a spectral gap assumption, Annals of Probability, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01706547

I. Grama and É. L. Page, Bounds in the Local Limit Theorem for a Random Walk Conditioned to Stay Positive, Modern Problems of Stochastic Analysis and Statistics, pp.1-21, 2017.
DOI : 10.1007/s00440-007-0124-8
URL : https://hal.archives-ouvertes.fr/hal-01449021

I. Grama, É. 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, issue.1, pp.1-55, 2014.
DOI : 10.4064/cm134-1-1

I. Grama, É. L. Page, and M. Peigné, Conditioned limit theorems for products of random matrices. Probability Theory and Related Fields, pp.1-39
URL : https://hal.archives-ouvertes.fr/hal-01449023

Y. Guivarc-'h and É. L. Page, On spectral properties of a family of transfer operators and convergence to stable laws for affine random walks. Ergodic Theory and Dynamical Systems, pp.423-446, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00360831

Y. Guivarc-'h and Q. Liu, Propriétés asymptotiques des processus de branchement en environnement aléatoire, Comptes Rendus de l'Académie des Sciences-Series I- Mathematics, pp.339-344, 2001.

G. H. Hardy, Divergent series, 1949.

T. E. Harris, The theory of branching processes, 1963.
DOI : 10.1007/978-3-642-51866-9

D. L. Iglehart, Functional central limit theorems for random walks conditioned to stay positive. The Annals of Probability, pp.608-619, 1974.

D. L. Iglehart, Random walks with negative drift conditioned to stay positive, Journal of Applied Probability, vol.3, issue.04, pp.742-751, 1974.
DOI : 10.1017/S0021900200094730

C. T. Ionescu-tulcea and G. Marinescu, Theorie Ergodique Pour Des Classes D'Operations Non Completement Continues, The Annals of Mathematics, vol.52, issue.1, pp.140-147, 1950.
DOI : 10.2307/1969514

T. Kato, Perturbation Theory for Linear Operators, 1976.

J. Komlós, P. Major, and G. Tusnády, An approximation of partial sums of independent RV'-s, and the sample DF. I. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, pp.111-131, 1975.

J. Komlós, P. Major, and G. Tusnády, An approximation of partial sums of independent RV's, and the sample DF. II. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, pp.33-58, 1976.

M. Kozlov, On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random Environment, Theory of Probability & Its Applications, pp.791-804, 1977.
DOI : 10.1137/1121091

É. and L. Page, Theoremes limites pour les produits de matrices aleatoires, Probability Measures on Groups, pp.258-303, 1982.
DOI : 10.1137/1110002

É. , L. Page, and M. Peigné, A local limit theorem on the semi-direct product of R * + and R d, Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.223-252, 1997.

É. , L. Page, and Y. Ye, The survival probability of a critical branching process in a Markovian random environment, Comptes Rendus Mathematique, vol.348, pp.5-6301, 2010.

P. Lévy, Processus stochastiques et mouvement brownien, 1965.

Q. Liu, On the survival probability of a branching process in a random environment, Annales de l'I.H.P. Probabilités et statistiques, pp.1-10, 1996.

M. F. Norman, Markov processes and learning models, 1972.

E. Presman, Boundary problems for sums of lattice random variables, defined on a finite regular markov chain. Theory of Probability and Its Applications, pp.323-328, 1967.

E. Presman, Methods of factorization and a boundary problems for sums of random variables defined on a markov chain, Izvestija Akademii Nauk SSSR, vol.33, pp.861-990, 1969.

W. L. Smith and W. E. Wilkinson, On Branching Processes in Random Environments, The Annals of Mathematical Statistics, vol.40, issue.3, pp.814-827, 1969.
DOI : 10.1214/aoms/1177697589

W. L. Smith and W. E. Wilkinson, Branching processes in Markovian environments, Duke Mathematical Journal, vol.38, issue.4, pp.749-763, 1970.
DOI : 10.1215/S0012-7094-71-03891-9

F. Spitzer, A combinatorial lemma and its application to probability theory. Transactions of the, pp.323-339, 1956.

F. Spitzer, A Tauberian theorem and its probability interpretation. Transactions of the, pp.150-169, 1960.
DOI : 10.2307/1993283

F. Spitzer, Principles of random walk. The University Series in Higher Mathematics, 1964.

C. Stone, A Local Limit Theorem for Nonlattice Multi-Dimensional Distribution Functions, The Annals of Mathematical Statistics, vol.36, issue.2, pp.546-551, 1965.
DOI : 10.1214/aoms/1177700165

N. Th and . Varopoulos, Potential theory in conical domains, Mathematical Proceedings of the Cambridge Philosophical Society, vol.125, issue.2, pp.335-384, 1999.

N. Th and . Varopoulos, Potential theory in conical domains, II. Mathematical Proceedings of the Cambridge Philosophical Society, vol.129, issue.2, pp.301-320, 2000.

N. Th and . Varopoulos, Potential Theory in Lipschitz Domains, Canadian Journal of Mathematics, vol.53, issue.5, pp.1057-1120, 2001.

V. A. Vatutin and V. Wachtel, Local probabilities for random walks conditioned to stay positive. Probability Theory and Related Fields, pp.177-217, 2008.
DOI : 10.1007/s00440-007-0124-8
URL : http://arxiv.org/pdf/0711.1302