V. Barbu and N. Limnios, Maximum likelihood estimation for hidden semi-Markov models, Comptes Rendus Mathematique, vol.342, issue.3, 2006.
DOI : 10.1016/j.crma.2005.12.013

V. Barbu and N. Limnios, Semi-Markov Chains and Hidden Semi-Markov Models toward Applications, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00530330

L. Baum, T. Petrie, G. Soules, and N. Weiss, A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains, The Annals of Mathematical Statistics, vol.41, issue.1, pp.164-171, 1970.
DOI : 10.1214/aoms/1177697196

L. E. Baum and T. Petrie, Statistical Inference for Probabilistic Functions of Finite State Markov Chains, The Annals of Mathematical Statistics, vol.37, issue.6, 1966.
DOI : 10.1214/aoms/1177699147

R. Bhar and S. Hamori, Hidden Markov Models: Applications to Financial Economics, 2004.

J. Booth and J. Hobert, Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.1, pp.61-265, 1999.
DOI : 10.1111/1467-9868.00176

J. Booth, J. Hobert, and W. Jank, A survey of Monte Carlo algorithms for maximizing the likelihood of a two-stage hierarchical model, Statistical Modelling, vol.1, issue.4, pp.333-349, 2001.
DOI : 10.1191/147108201128249

R. Boyles, On the convergence of EM algorithm, Journal of the Royal Statistical Society, Series B, vol.45, pp.47-50, 1983.

J. Bulla, Application of hidden Markov models and hidden semi-Markov models to financial time series. Thesis, 2006.

J. Bulla and I. Bulla, Stylized facts of financial time series and hidden semi-Markov models, Computational Statistics & Data Analysis, vol.51, issue.4, pp.2192-2209, 2006.
DOI : 10.1016/j.csda.2006.07.021

J. Bulla, I. Bulla, and O. Nenadi´cnenadi´c, hsmm ??? An R package for analyzing hidden semi-Markov models, Computational Statistics & Data Analysis, vol.54, issue.3, 2008.
DOI : 10.1016/j.csda.2008.08.025

B. Caffo, W. Jank, and G. Jones, Ascent-based Monte Carlo expectation- maximization, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.11, issue.2, pp.235-252, 2005.
DOI : 10.1111/1467-9868.00334

O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models, 2005.

G. Celeux and J. Diebolt, The SEM algorithm: a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem, Computational Statistics Quarterly, vol.2, pp.73-82, 1985.

K. Chan and J. Ledolter, Monte Carlo EM Estimation for Time Series Models Involving Counts, Journal of the American Statistical Association, vol.75, issue.429, pp.242-252, 1995.
DOI : 10.1080/01621459.1995.10476508

B. Delyon, V. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm, Annals of Statistics, vol.27, pp.94-128, 1999.

A. Dempster, N. Laird, and D. Rubin, Maximum Likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society. Series B, vol.39, pp.1-38, 1977.

R. Durbin, S. Eddy, A. Krogh, and G. Mitchison, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids, 1998.
DOI : 10.1017/CBO9780511790492

Y. Ephraim and N. Merhav, Hidden Markov processes, IEEE Transactions on Information Theory, vol.48, issue.6, pp.1518-1569, 2002.
DOI : 10.1109/TIT.2002.1003838

J. Ferguson, Variable duration models for speech, Proc. of the symposium on the Application of Hidden Markov Models to Text and Speech, pp.143-179, 1980.

M. Gu and H. Zhu, Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.2, pp.339-355, 2001.
DOI : 10.1111/1467-9868.00289

Y. Guédon, Estimating Hidden Semi-Markov Chains From Discrete Sequences, Journal of Computational and Graphical Statistics, vol.12, issue.3, pp.604-639, 2003.
DOI : 10.1198/1061860032030

Y. Guédon, Hidden hybrid Markov/semi-Markov chains, Computational Statistics & Data Analysis, vol.49, issue.3, pp.663-688, 2005.
DOI : 10.1016/j.csda.2004.05.033

Y. Guédon, Exploring the state sequence space for hidden Markov and semi-Markov chains, Computational Statistics & Data Analysis, vol.51, issue.5, pp.2379-2409, 2007.
DOI : 10.1016/j.csda.2006.03.015

Y. Guédon and C. Cocozza-thivent, Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme, Computer Speech & Language, vol.4, issue.2, pp.167-192, 1990.
DOI : 10.1016/0885-2308(90)90003-O

W. Jank, Stochastic Variants of EM: Monte Carlo, Quasi?Monte Carlo and More, Proc. of the American Statistical Association, 2005.

W. Jank, The EM algorithm, Its Stochastic Implementation and Global Optimization: Some Challenges and Opportunities for OR, Topics in Modeling, Optimization and Decision Technologies: Honoring Saul Gass' Contributions to Operation Research, pp.367-392, 2006.

W. Jank, Implementing and Diagnosing the Stochastic Approximation EM Algorithm, Journal of Computational and Graphical Statistics, vol.15, issue.4, pp.803-829, 2006.
DOI : 10.1198/106186006X157469

A. Krogh, M. Brown, I. S. Mian, K. Sjflander, and D. Haussler, Hidden Markov Models in Computational Biology, Journal of Molecular Biology, vol.235, issue.5, pp.1501-1531, 1994.
DOI : 10.1006/jmbi.1994.1104

A. Krogh, I. Mian, and D. Haussler, DNA, Nucleic Acids Research, vol.22, issue.22, pp.4768-4778, 1994.
DOI : 10.1093/nar/22.22.4768

M. Lavielle and C. Meza, A parameter expansion version of the SAEM algorithm, Statistics and Computing, vol.99, issue.2, pp.121-130, 2007.
DOI : 10.1007/s11222-006-9007-6

R. Levine and G. Casella, Implementations of the Monte Carlo EM Algorithm, Journal of Computational and Graphical Statistics, vol.10, issue.3, pp.422-439, 2001.
DOI : 10.1198/106186001317115045

R. Levine and J. Fan, An automated (Markov chain) Monte Carlo EM algorithm, Journal of Statistical Computation and Simulation, vol.10, issue.5, pp.349-359, 2004.
DOI : 10.1214/aos/1176346060

S. Levinson, Continuously variable duration hidden Markov models for automatic speech recognition, Computer Speech & Language, vol.1, issue.1, pp.29-45, 1986.
DOI : 10.1016/S0885-2308(86)80009-2

J. Li and R. Gray, Image Segmentation and Compression using Hidden Markov models, 2000.
DOI : 10.1007/978-1-4615-4497-5

G. J. Mclachlan and T. Krishnan, The EM Algorithm and Extensions, 2008.

B. Polyak and A. Juditsky, Acceleration of Stochastic Approximation by Averaging, SIAM Journal on Control and Optimization, vol.30, issue.4, 1992.
DOI : 10.1137/0330046

R. Pyke, Markov Renewal Processes: Definitions and Preliminary Properties, The Annals of Mathematical Statistics, vol.32, issue.4, pp.1231-1242, 1961.
DOI : 10.1214/aoms/1177704863

L. R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proc. IEEE, pp.257-284, 1989.

L. R. Rabiner and B. H. Juang, Fundamentals of Speech Recognition, 1993.

J. Sansom, A Hidden Markov Model for Rainfall Using Breakpoint Data, Journal of Climate, vol.11, issue.1, pp.42-53, 1998.
DOI : 10.1175/1520-0442(1998)011<0042:AHMMFR>2.0.CO;2

J. Sansom and P. Thomson, Fitting hidden semi-Markov models to breakpoint rainfall data, Journal of Applied Probability, vol.39, issue.A, pp.142-157, 2001.
DOI : 10.1175/1520-0442(1995)008<0624:RDASVU>2.0.CO;2

S. Trevezas and N. Limnios, Maximum likelihood estimation for general hidden semi-Markov processes with backward recurrence time dependence, Journal of Mathematical Sciences, vol.38, issue.3, pp.105-125, 2009.
DOI : 10.1007/s10958-009-9675-9

URL : https://hal.archives-ouvertes.fr/inria-00577955

G. Wei and M. Tanner, A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, vol.51, issue.411, pp.699-704, 1990.
DOI : 10.1214/aos/1176346060

C. Wu, On the Convergence Properties of the EM Algorithm, The Annals of Statistics, vol.11, issue.1, pp.95-103, 1983.
DOI : 10.1214/aos/1176346060