J. L. Doob, Conditional brownian motion and the boundary limits of harmonic functions, Bulletin de la Société mathématique de France, vol.79, pp.431-458, 1957.
DOI : 10.24033/bsmf.1494

J. L. Doob, Classical Potential Theory and Its Probabilistic Counterpart, 1984.

F. Baudoin, Conditioned stochastic differential equations: theory, examples and application to finance, Stochastic Processes and their Applications, vol.100, issue.1-2, pp.109-145, 2002.
DOI : 10.1016/S0304-4149(02)00109-6

D. Gasbarra, T. Sottinen, and E. Valkeila, Gaussian Bridges, Stochastic Analysis and Applications, Abel Symposia, pp.361-382, 2007.
DOI : 10.1007/978-3-540-70847-6_15

T. Sottinen and A. Yazigi, Generalized Gaussian bridges, Stochastic Processes and their Applications, vol.124, issue.9, pp.3084-3105, 2014.
DOI : 10.1016/j.spa.2014.04.002

E. Schrödinger, ¨ Uber die Umkehrung der Naturgesetze, Sitzungsber. Preuss. Akad. Wiss. Phys.-Math

E. Schrödinger, Sur la théorie relativiste de l'´ electron et l'interprétation de la mécanique quantique, Ann. Inst. Henri Poincaré, vol.2, pp.269-319, 1932.

B. Jamison, The Markov processes of Schr???dinger, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.22, issue.4, pp.323-331, 1975.
DOI : 10.1007/BF00535844

J. C. Zambrini, Stochastic mechanics according to E. Schr??dinger, Physical Review A, vol.33, issue.3, pp.1532-1548, 1986.
DOI : 10.1103/PhysRevA.33.1532

J. N. Darroch and E. Seneta, On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains, Journal of Applied Probability, vol.84, issue.01, pp.88-100, 1965.
DOI : 10.1214/aoms/1177705139

J. N. Darroch and E. Seneta, On quasi-stationary distributions in absorbing continuous-time finite Markov chains, Journal of Applied Probability, vol.28, issue.01, pp.192-196, 1967.
DOI : 10.1111/j.1467-842X.1966.tb00168.x

D. Villemonais, Quasi-stationary distributions and population processes, Prob. Surveys, vol.9, pp.340-410, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00653834

E. A. Van-doorn and P. K. Pollett, Quasi-stationary distributions for discrete-state models, European Journal of Operational Research, vol.230, issue.1, pp.1-14, 2013.
DOI : 10.1016/j.ejor.2013.01.032

O. A. Vasicek, A Conditional Law of Large Numbers, The Annals of Probability, vol.8, issue.1, pp.142-147, 1980.
DOI : 10.1214/aop/1176994830

J. M. Van-campenhout and T. M. Cover, Maximum entropy and conditional probability, IEEE Transactions on Information Theory, vol.27, issue.4, pp.483-489, 1981.
DOI : 10.1109/TIT.1981.1056374

I. Csiszar, Sanov Property, Generalized $I$-Projection and a Conditional Limit Theorem, The Annals of Probability, vol.12, issue.3, pp.768-793, 1984.
DOI : 10.1214/aop/1176993227

P. Diaconis and D. Freedman, A dozen de Finetti-style results in search of a theory, Ann. Inst. Henri Poincare B: Prob. Stat, vol.23, pp.397-423, 1987.

P. Diaconis and D. A. Freedman, Conditional limit theorems for exponential families and finite versions of de Finetti's theorem, Journal of Theoretical Probability, vol.93, issue.4, pp.381-410, 1988.
DOI : 10.1007/BF01048727

A. Dembo and O. Zeitouni, Refinements of the Gibbs conditioning principle, Probability Theory and Related Fields, vol.36, issue.1, pp.1-14, 1996.
DOI : 10.1007/BF01303799

I. Csiszár, T. M. Cover, and B. Choi, Conditional limit theorems under Markov conditioning, IEEE Transactions on Information Theory, vol.33, issue.6, pp.788-801, 1987.
DOI : 10.1109/TIT.1987.1057385

V. S. Borkar, S. Juneja, and A. A. Kherani, Peformance Analysis Conditioned on Rare Events: An Adaptive Simulation Scheme, Communications in Information and Systems, vol.3, issue.4, pp.259-278, 2004.
DOI : 10.4310/CIS.2003.v3.n4.a3

J. A. Bucklew, Introduction to Rare Event Simulation, 2004.
DOI : 10.1007/978-1-4757-4078-3

W. Feller, An Introduction to Probability Theory and its Applications, 1970.

C. Giardina, J. Kurchan, and L. Peliti, Direct Evaluation of Large-Deviation Functions, Physical Review Letters, vol.96, issue.12, p.120603, 2006.
DOI : 10.1103/PhysRevLett.96.120603
URL : https://hal.archives-ouvertes.fr/hal-00160781

V. Lecomte and J. Tailleur, A numerical approach to large deviations in continuous time, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.03, p.3004, 2007.
DOI : 10.1088/1742-5468/2007/03/P03004
URL : https://hal.archives-ouvertes.fr/hal-00160784

J. Tailleur and V. Lecomte, Simulation of large deviation functions using population dynamics, AIP Conference Proceedings, pp.212-219, 2009.
DOI : 10.1063/1.3082284

P. and D. Moral, Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications, Probability and Its Applications, 2004.

W. H. Fleming, Exit probabilities and optimal stochastic control, Applied Mathematics & Optimization, vol.17, issue.1, pp.329-346, 1978.
DOI : 10.1007/BF01442148

W. H. Fleming, Logarithmic transformations and stochastic control, Advances in Filtering and Optimal Stochastic Control, pp.131-141, 1982.
DOI : 10.1007/BFb0004532

W. H. Fleming, A stochastic control approach to some large deviations problems, Recent Mathematical Methods in Dynamic Programming, pp.52-66, 1985.
DOI : 10.1080/17442508308833285

W. H. Fleming and S. Sheu, Stochastic variational formula for fundamental solutions of parabolic PDE, Applied Mathematics & Optimization, vol.22, issue.1, pp.193-204, 1985.
DOI : 10.1007/BF01442207

M. Kac, On distributions of certain Wiener functionals, Transactions of the American Mathematical Society, vol.65, issue.1, pp.1-13, 1949.
DOI : 10.1090/S0002-9947-1949-0027960-X

D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 1999.

S. Sheu, Stochastic control and principal eigenvalue, pp.191-211, 1984.

W. H. Fleming, S. J. Sheub, and H. M. Soner, A remark on the large deviations of an ergodic markov process, Stochastics, vol.11, issue.3-4, pp.187-199, 1987.
DOI : 10.1007/BFb0004532

W. H. Fleming and S. Sheu, Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential, The Annals of Probability, vol.25, issue.4, pp.1953-1994, 1997.
DOI : 10.1214/aop/1023481117

W. H. Fleming and W. M. Mceneaney, Risk sensitive optimal control and differential games, Stochastic Theory and Adaptive Control, pp.185-197, 1992.
DOI : 10.1007/BFb0113240

W. Fleming and W. Mceneaney, Risk-Sensitive Control on an Infinite Time Horizon, SIAM Journal on Control and Optimization, vol.33, issue.6, pp.1881-1915, 1995.
DOI : 10.1137/S0363012993258720

P. Dupuis and W. Mceneaney, Risk-Sensitive and Robust Escape Criteria, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.2021-2049, 1997.
DOI : 10.1137/S0363012995281626

T. Nemoto and S. Sasa, Thermodynamic formula for the cumulant generating function of time-averaged current, Physical Review E, vol.84, issue.6, p.61113, 2011.
DOI : 10.1103/PhysRevE.84.061113

T. Nemoto and S. Sasa, Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems, Physical Review E, vol.83, issue.3, p.30105, 2011.
DOI : 10.1103/PhysRevE.83.030105

T. Nemoto and S. Sasa, Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure, Physical Review Letters, vol.112, issue.9, p.90602, 2014.
DOI : 10.1103/PhysRevLett.112.090602

H. Touchette, The large deviation approach to statistical mechanics, Physics Reports, vol.478, issue.1-3, pp.1-69, 2009.
DOI : 10.1016/j.physrep.2009.05.002

M. I. Freidlin and A. D. , Random Perturbations of Dynamical Systems, Grundlehren der Mathematischen Wissenschaften, vol.260, 1984.

C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 1985.

H. Risken, The Fokker-Planck Equation: Methods of Solution and Application, 2nd ed., Journal of Applied Mechanics, vol.58, issue.3, 1996.
DOI : 10.1115/1.2897281

R. M. Evans, Rules for Transition Rates in Nonequilibrium Steady States, Physical Review Letters, vol.92, issue.15, p.150601, 2004.
DOI : 10.1103/PhysRevLett.92.150601

R. M. Evans, Detailed balance has a counterpart in non-equilibrium steady states, Journal of Physics A: Mathematical and General, vol.38, issue.2, pp.293-313, 2005.
DOI : 10.1088/0305-4470/38/2/001

R. M. Evans, Statistical physics of shear flow: a non-equilibrium problem, Contemporary Physics, vol.51, issue.5, pp.413-427, 2010.
DOI : 10.1021/ma9004346

C. Dellago, P. G. Bolhuis, and P. L. Geissler, Transition path sampling, Adv. Chem. Phys, vol.123, pp.1-78, 2003.
DOI : 10.1007/978-1-4020-3286-8_79
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.2833

C. Dellago, P. G. Bolhuis, and P. L. Geissler, Transition Path Sampling Methods, Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, 2006.
DOI : 10.1007/3-540-35273-2_10

C. Dellago and P. Bolhuis, Transition Path Sampling and Other Advanced Simulation Techniques for Rare Events, Advanced Computer Simulation Approaches for Soft Matter Sciences III , Advances in Polymer Science, vol.221, pp.167-233, 2009.
DOI : 10.1007/978-3-540-87706-6_3

E. Vanden-eijnden, Transition path theory, Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, pp.453-493, 2006.

D. Chandler and J. P. Garrahan, Dynamics on the Way to Forming Glass: Bubbles in Space-Time, Annual Review of Physical Chemistry, vol.61, issue.1, pp.191-217, 2010.
DOI : 10.1146/annurev.physchem.040808.090405

L. O. Hedges, R. L. Jack, J. P. Garrahan, and D. Chandler, Dynamic Order-Disorder in Atomistic Models of Structural Glass Formers, Science, vol.323, issue.5919, pp.1309-1313, 2009.
DOI : 10.1126/science.1166665

R. L. Jack and P. Sollich, Large Deviations and Ensembles of Trajectories in Stochastic Models, Progress of Theoretical Physics Supplement, vol.184, pp.304-317, 2010.
DOI : 10.1143/PTPS.184.304

V. Lecomte, C. Appert-rolland, and F. Van-wijland, Chaotic Properties of Systems with Markov Dynamics, Physical Review Letters, vol.95, issue.1, p.10601, 2005.
DOI : 10.1103/PhysRevLett.95.010601
URL : https://hal.archives-ouvertes.fr/hal-00016457

V. Lecomte, C. Appert-rolland, and F. Van-wijland, Thermodynamic Formalism for Systems with Markov Dynamics, Journal of Statistical Physics, vol.102, issue.1, pp.51-106, 2007.
DOI : 10.1007/s10955-006-9254-0
URL : https://hal.archives-ouvertes.fr/hal-00107948

J. P. Garrahan and I. Lesanovsky, Thermodynamics of Quantum Jump Trajectories, Physical Review Letters, vol.104, issue.16, p.160601, 2010.
DOI : 10.1103/PhysRevLett.104.160601

J. P. Garrahan, A. D. Armour, and I. Lesanovsky, Quantum trajectory phase transitions in the micromaser, Physical Review E, vol.84, issue.2, p.21115, 2011.
DOI : 10.1103/PhysRevE.84.021115

C. Ates, B. Olmos, J. P. Garrahan, and I. Lesanovsky, Dynamical phases and intermittency of the dissipative quantum Ising model, Physical Review A, vol.85, issue.4, p.43620, 2012.
DOI : 10.1103/PhysRevA.85.043620

S. Genway, J. P. Garrahan, I. Lesanovsky, and A. D. Armour, Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator, Physical Review E, vol.85, issue.5, p.51122, 2012.
DOI : 10.1103/PhysRevE.85.051122

J. M. Hickey, S. Genway, I. Lesanovsky, and J. P. Garrahan, Thermodynamics of quadrature trajectories in open quantum systems, Physical Review A, vol.86, issue.6, p.63824, 2012.
DOI : 10.1103/PhysRevA.86.063824

R. Chetrite and H. Touchette, Nonequilibrium Microcanonical and Canonical Ensembles and Their Equivalence, Physical Review Letters, vol.111, issue.12, p.120601, 2013.
DOI : 10.1103/PhysRevLett.111.120601
URL : https://hal.archives-ouvertes.fr/hal-00915479

H. Spohn, Large Scale Dynamics of Interacting Particles, 1991.
DOI : 10.1007/978-3-642-84371-6

C. Kipnis and C. Landim, Scaling Limits of Interacting Particle Systems, Grundlheren der mathematischen Wissenschaften, 1999.

T. M. Liggett, Interacting Particle Systems, Classics in Mathematics, 2004.
DOI : 10.1007/b138374
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.3652

B. Derrida, Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7023, 2007.
DOI : 10.1088/1742-5468/2007/07/P07023

L. Bertini, A. De-sole, D. Gabrielli, G. Jona-lasinio, and C. Landim, Stochastic interacting particle systems out of equilibrium, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7014, 2007.
DOI : 10.1088/1742-5468/2007/07/P07014

K. Jacobs, Stochastic Processes for Physicists: Understanding Noisy Systems, 2010.
DOI : 10.1017/CBO9780511815980

P. L. Krapivsky, S. Redner, and E. Ben-naim, A Kinetic View of Statistical Physics, 2010.
DOI : 10.1017/CBO9780511780516

E. Nelson, Dynamical Theories of Brownian Motion, 1967.

W. J. Anderson, Continuous-Time Markov Chains: An Applications-Oriented Approach, 1991.
DOI : 10.1007/978-1-4612-3038-0

D. Applebaum, Lévy Processes and Stochastic Calculus, 2009.

K. Sato, Lévy processes and Infinite Divisibility, Cambridge Studies in Advanced Mathematics, 1999.

L. Hörmander, Hypoelliptic second order differential equations, Acta Mathematica, vol.119, issue.0, pp.147-171, 1967.
DOI : 10.1007/BF02392081

P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, Proc. Inter. Symp. Stoch. Diff. Equations, pp.195-263, 1976.

J. L. Lebowitz and H. Spohn, A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, Journal of Statistical Physics, vol.95, issue.1/2, pp.333-365, 1999.
DOI : 10.1023/A:1004589714161

C. Maes and K. Neto?n´neto?n´y, Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states, EPL (Europhysics Letters), vol.82, issue.3, p.82, 2008.
DOI : 10.1209/0295-5075/82/30003

M. Baiesi, C. Maes, and B. Wynants, Fluctuations and Response of Nonequilibrium States, Physical Review Letters, vol.103, issue.1, p.10602, 2009.
DOI : 10.1103/PhysRevLett.103.010602

C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Physical Review E, vol.56, issue.5, pp.5018-5035, 1997.
DOI : 10.1103/PhysRevE.56.5018

G. E. Crooks, Nonequilibrium measurements of free energy differences for microscopically reversible markovian systems, Journal of Statistical Physics, vol.90, issue.5/6, pp.1481-1487, 1998.
DOI : 10.1023/A:1023208217925

C. Maes, K. Neto?n´neto?n´y, and B. Wynants, Steady state statistics of driven diffusions, Physica A: Statistical Mechanics and its Applications, vol.387, issue.12, pp.2675-2689, 2008.
DOI : 10.1016/j.physa.2008.01.097

V. Chernyak, M. Chertkov, S. Malinin, and R. Teodorescu, Non-Equilibrium Thermodynamics and Topology of??Currents, Journal of Statistical Physics, vol.17, issue.5, pp.109-147, 2009.
DOI : 10.1007/s10955-009-9832-z

A. Basu, T. Bhattacharyya, and V. S. Borkar, A Learning Algorithm for Risk-Sensitive Cost, Mathematics of Operations Research, vol.33, issue.4, pp.880-898, 2008.
DOI : 10.1287/moor.1080.0324

F. Hollander, Large Deviations, Fields Institute Monograph (Amer, Math. Soc., Providence, R.I, 2000.

A. De-la-fortelle, Large deviation principle for Markov chains in continuous time, Problems of Information Transmission, vol.37, issue.2, pp.120-139, 2001.
DOI : 10.1023/A:1010470024888
URL : https://hal.archives-ouvertes.fr/inria-00072776

L. Bertini, A. Faggionato, and D. Gabrielli, Large deviations of the empirical flow for continuous time Markov chains, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.51, issue.3, p.1210, 2004.
DOI : 10.1214/14-AIHP601

J. T. Lewis, C. Pfister, and G. W. Sullivan, The equivalence of ensembles for lattice systems: Some examples and a counterexample, Journal of Statistical Physics, vol.85, issue.1-2, pp.397-419, 1994.
DOI : 10.1007/BF02186849

J. T. Lewis, C. Pfister, and W. G. Sullivan, Entropy, concentration of probability and conditional limit theorem, Markov Proc. Rel, pp.319-386, 1995.

H. Touchette, Equivalence and Nonequivalence of Ensembles: Thermodynamic, Macrostate, and Measure Levels, Journal of Statistical Physics, vol.61, issue.5, 2014.
DOI : 10.1007/s10955-015-1212-2

C. R. Maccluer, The Many Proofs and Applications of Perron's Theorem, SIAM Review, vol.42, issue.3, pp.487-498, 2000.
DOI : 10.1137/S0036144599359449

M. G. Krein and M. A. Rutman, Linear operators leaving a cone in a Banach space, Am. Math. Soc. Transl, vol.26, p.128, 1950.

V. Lecomte, Thermodynamique des histoires et fluctuations hors d'´ equilibre, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00198144

R. Chetrite and S. Gupta, Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale, Journal of Statistical Physics, vol.73, issue.6, pp.543-584, 2011.
DOI : 10.1007/s10955-011-0184-0
URL : https://hal.archives-ouvertes.fr/hal-00915480

H. Kunita, Absolute Continuity of Markov Processes and Generators, Nagoya Mathematical Journal, vol.15, pp.1-26, 1969.
DOI : 10.1137/1111036

K. Itô and S. Watanabe, Transformation of Markov processes by multiplicative functionals, Annales de l???institut Fourier, vol.15, issue.1, pp.13-30, 1965.
DOI : 10.5802/aif.192

Z. Palmowski and T. Rolski, A technique for exponential change of measure for Markov processes, pp.767-785, 2002.

P. Diaconis and L. Miclo, On characterizations of Metropolis type algorithms in continuous time, ALEA Lat. Am. J. Probab. Math. Stat, vol.6, pp.199-238, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00353845

P. A. Meyer and W. A. Zheng, Construction de processus de Nelson reversibles, Séminaire de Probabilités XIX, pp.12-26, 1983.
DOI : 10.1017/S0027763000012484

W. Bernard and H. B. Callen, Irreversible Thermodynamics of Nonlinear Processes and Noise in Driven Systems, Reviews of Modern Physics, vol.31, issue.4, pp.1017-1044, 1959.
DOI : 10.1103/RevModPhys.31.1017

H. B. Callen and T. A. Welton, Irreversibility and Generalized Noise, Physical Review, vol.83, issue.1, pp.34-40, 1951.
DOI : 10.1103/PhysRev.83.34

R. Kubo, The fluctuation-dissipation theorem, Reports on Progress in Physics, vol.29, issue.1, p.255, 1966.
DOI : 10.1088/0034-4885/29/1/306

E. Lippiello, F. Corberi, A. Sarracino, and M. Zannetti, Nonlinear response and fluctuation-dissipation relations, Physical Review E, vol.78, issue.4, p.41120, 2008.
DOI : 10.1103/PhysRevE.78.041120
URL : http://arxiv.org/abs/0809.3328

T. Speck and U. Seifert, Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state, Europhysics Letters (EPL), vol.74, issue.3, p.391, 2006.
DOI : 10.1209/epl/i2005-10549-4

M. Baiesi, C. Maes, and B. Wynants, Nonequilibrium Linear Response for Markov Dynamics, I: Jump Processes and Overdamped Diffusions, Journal of Statistical Physics, vol.248, issue.5-6, pp.1094-1116, 2009.
DOI : 10.1007/s10955-009-9852-8

M. Baiesi, E. Boksenbojm, C. Maes, and B. Wynants, Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics, Journal of Statistical Physics, vol.74, issue.3, pp.492-505, 2010.
DOI : 10.1007/s10955-010-9951-6

U. Seifert and T. Speck, Fluctuation-dissipation theorem in nonequilibrium steady states, EPL (Europhysics Letters), vol.89, issue.1, p.10007, 2010.
DOI : 10.1209/0295-5075/89/10007

R. Chetrite, G. Falkovich, and K. Gawedzki, Fluctuation relations in simple examples of nonequilibrium steady states, J. Stat. Mech, p.8005, 2008.

R. Chetrite and K. Gawedzki, Eulerian and Lagrangian Pictures of Non-equilibrium Diffusions, Journal of Statistical Physics, vol.71, issue.5-6, pp.890-916, 2009.
DOI : 10.1007/s10955-009-9803-4

C. Jarzynski, Nonequilibrium Equality for Free Energy Differences, Physical Review Letters, vol.78, issue.14, pp.2690-2693, 1997.
DOI : 10.1103/PhysRevLett.78.2690
URL : http://arxiv.org/abs/cond-mat/9610209

D. J. Evans, E. G. Cohen, and G. P. Morriss, Probability of second law violations in shearing steady states, Physical Review Letters, vol.71, issue.15, pp.2401-2404, 1993.
DOI : 10.1103/PhysRevLett.71.2401

G. Gallavotti and E. G. Cohen, Dynamical Ensembles in Nonequilibrium Statistical Mechanics, Physical Review Letters, vol.74, issue.14, pp.2694-2697, 1995.
DOI : 10.1103/PhysRevLett.74.2694

G. Gallavotti and E. G. Cohen, Dynamical ensembles in stationary states, Journal of Statistical Physics, vol.78, issue.3, pp.931-970, 1995.
DOI : 10.1007/BF02179860

F. J. Dyson, A Brownian???Motion Model for the Eigenvalues of a Random Matrix, Journal of Mathematical Physics, vol.3, issue.6, pp.1191-1198, 1962.
DOI : 10.1063/1.1703862

D. J. Grabiner, Brownian motion in a Weyl chamber, non-colliding particles, and random matrices, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.35, issue.2, pp.177-204, 1999.
DOI : 10.1016/S0246-0203(99)80010-7

N. O. Connell, Random matrices, non-colliding processes and queues, Séminaire de Probabilités XXXVI, pp.165-182, 2003.
DOI : 10.1007/978-3-540-36107-7_3
URL : https://hal.archives-ouvertes.fr/hal-00136037

H. Touchette, Ensemble equivalence for general many-body systems, EPL (Europhysics Letters), vol.96, issue.5, p.50010, 2011.
DOI : 10.1209/0295-5075/96/50010

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

T. R. Gingrich, S. Vaikuntanathan, and P. L. Geissler, Heterogeneity-induced large deviations in activity and (in some cases) entropy production, Physical Review E, vol.90, issue.4, 2014.
DOI : 10.1103/PhysRevE.90.042123

N. Merhav and Y. Kafri, Bose???Einstein condensation in large deviations with applications to information systems, Journal of Statistical Mechanics: Theory and Experiment, vol.2010, issue.02, p.2011, 2010.
DOI : 10.1088/1742-5468/2010/02/P02011

R. J. Harris, V. Popkov, and G. M. Schütz, Dynamics of Instantaneous Condensation in the ZRP Conditioned on an Atypical Current, Entropy, vol.15, issue.11, pp.5065-5083, 2013.
DOI : 10.3390/e15115065

J. Szavits-nossan, M. R. Evans, and S. N. Majumdar, Constraint-Driven Condensation in Large Fluctuations of Linear Statistics, Physical Review Letters, vol.112, issue.2, p.20602, 2014.
DOI : 10.1103/PhysRevLett.112.020602
URL : https://hal.archives-ouvertes.fr/hal-00935509

A. Baule and R. M. Evans, Invariant Quantities in Shear Flow, Physical Review Letters, vol.101, issue.24, p.240601, 2008.
DOI : 10.1103/PhysRevLett.101.240601

A. Simha, R. M. Evans, and A. Baule, Properties of a nonequilibrium heat bath, Physical Review E, vol.77, issue.3, p.31117, 2008.
DOI : 10.1103/PhysRevE.77.031117

A. Baule and R. M. Evans, Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations, Journal of Statistical Mechanics: Theory and Experiment, vol.2010, issue.03, p.3030, 2010.
DOI : 10.1088/1742-5468/2010/03/P03030

V. Popkov, G. M. Schütz, and D. Simon, ASEP on a ring conditioned on enhanced flux, Journal of Statistical Mechanics: Theory and Experiment, vol.2010, issue.10, p.10007, 2010.
DOI : 10.1088/1742-5468/2010/10/P10007

V. Popkov and G. Schütz, Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux, Journal of Statistical Physics, vol.28, issue.1, pp.627-639, 2011.
DOI : 10.1007/s10955-011-0137-7

R. L. Jack and P. Sollich, Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories, Journal of Physics A: Mathematical and Theoretical, vol.47, issue.1, p.15003, 2014.
DOI : 10.1088/1751-8113/47/1/015003

M. Kne?evi´kne?evi´c and R. M. Evans, Numerical comparison of a constrained path ensemble and a driven quasisteady state, Physical Review E, vol.89, issue.1, p.12132, 2014.
DOI : 10.1103/PhysRevE.89.012132

J. Chen, H. Li, and S. Jian, Some limit theorems for absorbing Markov processes, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.34, p.345003, 2012.
DOI : 10.1088/1751-8113/45/34/345003

J. Chen and X. Deng, Large deviations and related problems for absorbing Markov chains, Stochastic Processes and their Applications, vol.123, issue.6, pp.2398-2418, 2013.
DOI : 10.1016/j.spa.2013.02.014

M. Bauer and F. Cornu, Affinity and Fluctuations in a Mesoscopic Noria, Journal of Statistical Physics, vol.107, issue.21, 2014.
DOI : 10.1007/s10955-014-0969-z
URL : https://hal.archives-ouvertes.fr/cea-00973196

H. D. Miller, A Convexity Property in the Theory of Random Variables Defined on a Finite Markov Chain, The Annals of Mathematical Statistics, vol.32, issue.4, pp.1260-1270, 1961.
DOI : 10.1214/aoms/1177704865