D. Aldous and P. Diaconis, Shuffling cards and stopping times, American Mathematical Monthly, vol.93, issue.5, pp.333-348, 1986.
DOI : 10.1080/00029890.1986.11971821

URL : https://cloudfront.escholarship.org/dist/prd/content/qt0k4654kx/qt0k4654kx.pdf?t=p3zsl7

D. Aldous and P. Diaconis, Strong uniform times and finite random walks, Advances in Applied Mathematics, vol.8, issue.1, pp.69-97, 1987.
DOI : 10.1016/0196-8858(87)90006-6

URL : https://doi.org/10.1016/0196-8858(87)90006-6

W. J. Anderson, Continuous-time Markov chains, Springer Series in Statistics : Probability and its Applications, 1991.

S. V. Anulova, Diffusion processes with singular characteristics, Stochastic differential systems (Proc. IFIP-WG 7/1 Working Conf., Vilnius, vol.25, pp.264-269, 1978.
DOI : 10.1007/bfb0004016

D. Bakry, I. Gentil, and M. Ledoux, Analysis and geometry of Markov diffusion operators, vol.348
URL : https://hal.archives-ouvertes.fr/hal-00929960

C. Springer, , 2014.

P. Barbe and M. Ledoux, Probabilité. Collection Enseignement sup. Mathématiques, 2007.

A. Berberian, La cité de la peur, une comédie familiale. Les Nuls, 1994.

P. Billingsley, Convergence of probability measures. Wiley Series in Probability and Statistics : Probability and Statistics, 1999.

H. E. Bray, Elementary properties of the Stieltjes integral, Ann. of Math, vol.20, issue.2, pp.177-186, 1919.

P. Brémaud, Gibbs fields, Monte Carlo simulation, and queues, Texts in Applied Mathematics, vol.31, 1999.

A. Bretto, A. Faisant, and F. Hennecart, Éléments de théorie des graphes. Collection IRIS

M. Brown and Y. Shao, Identifying coefficients in the spectral representation for first passage time distributions, Probability in the Engineering and Informational Sciences, vol.1, pp.69-74, 1987.

P. Carmona, F. Petit, and M. Yor, Beta-gamma random variables and intertwining relations between certain Markov processes, Revista Matemática Iberoamericana, vol.14, issue.2, pp.311-367, 1998.

D. Chafaï and A. Joulin, Intertwining and commutation relations for birth-death processes, Bernoulli, vol.19, issue.5A, pp.1855-1879, 2013.

B. Cloez and C. Delplancke, Intertwinings and Stein's magic factors for birth-death processes, 2016.

D. L. Cohn, Measure theory. Birkhäuser, 1980.

G. Copros, Existence condition of strong stationary times for continuous time markov chains on discrete graphs, Journal of Theoretical Probability, 2017.

K. Coulibaly, -. Pasquier, and L. Miclo, On the evolution by duality of domains on manifolds
URL : https://hal.archives-ouvertes.fr/hal-02009885

C. Dellacherie and P. Meyer, Probabilités et potentiel. Hermann, Paris, 1975. Chapitres I à IV, Édition entièrement refondue, Actualités Scientifiques et Industrielles, p.1372

P. Diaconis, Group representations in probability and statistics, vol.11, 1988.

P. Diaconis, The cutoff phenomenon in finite Markov chains, Proceedings of the National Academy of Sciences of the United States of America, vol.93, pp.1659-1664, 1996.

P. Diaconis and J. A. Fill, Examples for the theory of strong stationary duality with countable state spaces, Probability in the Engineering and Informational Sciences, vol.4, issue.2, pp.157-180, 1990.

P. Diaconis and J. A. Fill, Strong stationary times via a new form of duality, The Annals of Probability, vol.18, issue.4, pp.1483-1522, 1990.

P. Diaconis and L. Miclo, On times to quasi-stationarity for birth and death processes, Journal of Theoretical Probability, vol.22, issue.3, pp.558-586, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00164690

P. Diaconis and L. Saloff-coste, Separation cut-offs for birth and death chains, The Annals of Applied Probability, vol.16, issue.4, pp.2098-2122, 2006.

P. Diaconis and M. Shahshahani, Generating a random permutation with random transpositions, Probability Theory and Related Fields, vol.57, pp.159-179, 1981.

J. L. Doob, Stochastic processes

&. Chapman and . Hall, , 1953.

E. B. Dynkin, Markov processes, 1965.

N. Stewart, T. G. Ethier, and . Kurtz, Markov processes. Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, 1986.

W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Annals of Mathematics. Second Series, vol.55, pp.468-519, 1952.

J. A. Fill, Time to stationarity for a continuous-time Markov chain, Probability in the Engineering and Informational Sciences, vol.5, issue.1, pp.61-76, 1991.

J. A. Fill, Strong stationary duality for continuous-time Markov chains, I. Theory. Journal of Theoretical Probability, vol.5, issue.1, pp.45-70, 1992.

J. A. Fill, An interruptible algorithm for perfect sampling via Markov chains, The Annals of Applied Probability, vol.8, issue.1, pp.131-162, 1998.

J. A. Fill, On hitting times and fastest strong stationary times for skip-free and more general chains, Journal of Theoretical Probability, vol.22, issue.3, pp.587-600, 2009.

J. A. Fill, The passage time distribution for a birth-and-death chain : strong stationary duality gives a first stochastic proof, Journal of Theoretical Probability, vol.22, issue.3, pp.543-557, 2009.

J. A. Fill and J. Kahn, Comparison inequalities and fastest-mixing Markov chains, The Annals of Applied Probability, vol.23, issue.5, pp.1778-1816, 2013.

J. A. Fill and V. Lyzinski, Strong stationary duality for diffusion processes, Journal of Theoretical Probability, vol.29, issue.4, pp.1298-1338, 2016.

J. A. Fill, M. Machida, D. J. Murdoch, and J. S. Rosenthal, Extension of Fill's perfect rejection sampling algorithm to general chains (extended abstract), Monte Carlo methods, vol.26, pp.37-52, 1998.

M. Freidlin and S. Sheu, Diffusion processes on graphs : stochastic differential equations, large deviation principle. Probability Theory and Related Fields, vol.116, pp.181-220, 2000.

I. Mark, A. D. Freidlin, and . Wentzell, Diffusion processes on graphs and the averaging principle, The Annals of Probability, vol.21, issue.4, pp.2215-2245, 1993.

Y. Gong, Y. Mao, and C. Zhang, Hitting time distributions for denumerable birth and death processes, Journal of Theoretical Probability, vol.25, issue.4, pp.950-980, 2012.

D. Griffeath, A maximal coupling for Markov chains, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, vol.31, p.75, 1974.

E. Hille, Functional Analysis and Semi-Groups, vol.31, 1948.

N. Ikeda, S. Watanabe-;-kodansha, and L. , Stochastic differential equations and diffusion processes, vol.24, 1989.

S. Karlin and J. Mcgregor, Coincidence properties of birth and death processes, Pacific Journal of Mathematics, vol.9, issue.4, pp.1109-1140, 1959.

S. Karlin and H. M. Taylor, A first course in stochastic processes, 1975.

S. Karlin and H. M. Taylor, A second course in stochastic processes, 1981.

D. G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded markov chain, Ann. Math. Statist, vol.24, issue.3, p.1953

J. Harold, P. Kushner, and . Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, vol.24, 2001.

M. Ledoux, The geometry of Markov diffusion generators, Sciences de Toulouse. Mathématiques. Série, vol.6, issue.2, pp.305-366, 2000.

A. Lejay, On the constructions of the skew Brownian motion, Probab. Surv, vol.3, pp.413-466, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00000785

D. A. Levin, Y. Peres, and E. L. Wilmer, Markov chains and mixing times, 2009.

P. Lévy, Théorie de l'addition des variables aléatoires. Collection des monographies des probabilités, 1937.

T. M. Liggett, Continuous time Markov processes, Graduate Studies in Mathematics, vol.113, 2010.

P. Lorek and R. Szekli, Strong stationary duality for Möbius monotone Markov chains. Queueing Systems, Theory and Applications, vol.71, issue.1-2, pp.79-95, 2012.

P. Lorek and R. Szekli, Strong stationary duality for Möbius monotone Markov chains : examples, Probability and Mathematical Statistics, vol.36, issue.1, pp.75-97, 2016.

P. Lorek, F. Zagórski, and M. Kulis, Strong stationary times and its use in cryptography, 2017.

V. Lyzinski, Intertwinings, interlacing eigenvalues, and strong stationary duality for diffusions, ProQuest LLC, 2013.

Y. Mao and P. Zhao, Strong stationary duality for discrete time Möbius monotone Markov chains on Z d, Statistics & Probability Letters, vol.123, pp.183-192, 2017.

P. Matthews, Mixing rates for a random walk on the cube, Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods, vol.8, issue.4, pp.746-752, 1987.

P. Matthews, A strong uniform time for random transpositions, Journal of Theoretical Probability, vol.1, issue.4, pp.411-423, 1988.

P. Matthews, Some sample path properties of a random walk on the cube, Journal of Theoretical Probability, vol.2, issue.1, pp.129-146, 1989.

L. Miclo, Processus de markov inhomogènes finis

L. Miclo, On ergodic diffusions on continuous graphs whose centered resolvent admits a trace, Journal of Mathematical Analysis and Applications, vol.437, issue.2, pp.737-753, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00957019

L. Miclo, Strong stationary times for one-dimensional diffusions, vol.53, pp.957-996, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00909133

J. Møller and K. Schladitz, Extensions of Fill's algorithm for perfect simulation, Journal of the Royal Statistical Society. Series B. Statistical Methodology, vol.61, issue.4, pp.955-969, 1999.

B. Morris and Y. Peres, Evolving sets, mixing and heat kernel bounds, Probability Theory and Related Fields, vol.133, pp.245-266, 2005.

E. Nestoridis, Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement, 2017.

J. R. Norris, Markov chains, of Cambridge Series in Statistical and Probabilistic Mathematics, vol.2, 1998.

P. Patie, M. Savov, and Y. Zhao, Intertwining, Excursion Theory and Krein Theory of Strings for Non-self-adjoint Markov Semigroups, 2017.

J. W. Pitman, One-dimensional Brownian motion and the three-dimensional Bessel process, Advances in Applied Probability, vol.7, issue.3, pp.511-526, 1975.

I. Nicolai and . Portenko, Stochastic differential equations with generalized drift vector, Theory of Probability & Its Applications, vol.24, pp.338-353, 1980.

Y. V. Prokhorov, Convergence of random processes and limit theorems in probability theory. Theory of Probability & Its Applications, vol.1, pp.157-214, 1956.

G. James, D. B. Propp, and . Wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics, Proceedings of the Seventh International Conference on Random Structures and Algorithms, vol.9, pp.223-252, 1995.

D. Revuz and M. Yor, Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften, vol.293

. Springer-verlag, , 1999.

C. G. Leonard, J. W. Rogers, and . Pitman, Markov functions. The Annals of Probability, vol.9, pp.573-582, 1981.

G. Rota, On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, vol.2, pp.340-368, 1964.

. Walter-rudin, Real and complex analysis, 1966.

W. M. Schmidt, Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, 1991.

A. Lynn, J. A. Steen, J. Seebach, . Holt, W. Rinehart et al., , 1970.

W. Daniel, S. R. Stroock, and . Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math, vol.24, pp.147-225, 1971.

W. Daniel, S. R. Stroock, and . Srinivasa-varadhan, Diffusion processes with continuous coefficients, II. Communications on Pure and Applied Mathematics, vol.22, pp.479-530, 1969.

W. Daniel, S. R. Stroock, and . Srinivasa-varadhan, Multidimensional diffusion processes, Classics in Mathematics, 2006.

S. Takanobu, On the uniqueness of solutions of stochastic differential equations with singular drifts, Publ. Res. Inst. Math. Sci, vol.22, issue.5, pp.813-848, 1986.

S. Takanobu, On the existence of solutions of stochastic differential equations with singular drifts, vol.74, pp.295-315, 1987.

S. Takanobu and S. Watanabe, On the existence and uniqueness of diffusion processes with Wentzell's boundary conditions, J. Math. Kyoto Univ, vol.28, issue.1, pp.71-80, 1988.

E. Thönnes, Perfect simulation of some point processes for the impatient user, Advances in Applied Probability, vol.31, issue.1, pp.69-87, 1999.

H. Thorisson, Future independent times and Markov chains. Probability Theory and Related Fields, vol.78, pp.143-148, 1988.

E. A. Van-doorn, Stochastic monotonicity and queueing applications of birth-death processes, Lecture Notes in Statistics, vol.4, 1981.

A. D. Venttsel and &. , On boundary conditions for multidimensional diffusion processes, Theory of Probability & Its Applications, vol.4, pp.164-177, 1959.

S. Willard, General Topology, 1970.

M. Yor, Intertwinings of Bessel processes, 1988.

K. Yosida, On the differentiability and the representation of one-parameter semigroup of linear operators, Journal of the Mathematical Society of Japan, vol.1, issue.1, pp.15-21, 1948.