S. Asmussen, Applied probability and queues, 1987.

S. Asmussen, Risk theory in a Markovian environment, Scand. Actuar. J, vol.2, pp.69-100, 1989.

H. Bühlmann and A. Gisler, A course in credibility theory and its applications, 2005.

W. K. Ching, R. H. Chan, and X. Y. Zhou, Circulant Preconditioners for Markov-Modulated Poisson Processes and Their Applications to Manufacturing Systems, SIAM Journal on Matrix Analysis and Applications, vol.18, issue.2
DOI : 10.1137/S0895479895293442

J. D. Cole and S. R. Pfaff, A climatology of tropical cyclones affecting the Texas coast during El Niño/non-El Niño years: 1990-1996, 1997.

W. Fischer and K. S. Meier-hellstern, The Markov-modulated Poisson process (MMPP) cookbook , Perf, Eval, vol.18, pp.149-171, 1993.
DOI : 10.1016/0166-5316(93)90035-s

A. Guillou, S. Loisel, and G. Stupfler, Estimation of the parameters of a Markov-modulated loss process in insurance, Insurance: Mathematics and Economics, vol.53, issue.2, pp.388-404, 2013.
DOI : 10.1016/j.insmatheco.2013.07.003
URL : https://hal.archives-ouvertes.fr/hal-00589696

R. Helmers, I. W. Mangku, and R. Zitikis, A non-parametric estimator for the doubly periodic Poisson intensity function, Statistical Methodology, vol.4, issue.4, pp.481-492, 2007.
DOI : 10.1016/j.stamet.2007.02.002

G. Kesidis, J. Walrand, and C. Chang, Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEE/ACM Transactions on Networking, vol.1, issue.4, pp.424-428, 1993.
DOI : 10.1109/90.251894

D. Landreneau, Atlantic tropical storms and hurricanes affecting the United States: 1899-2000, NOAA Technical Memorandum NWS SR-206 (updated through, National Weather Service Office, 2001.

P. D. Lax, Linear Algebra and its applications, 2007.

B. G. Leroux, Maximum-likelihood estimation for hidden Markov models, Stochastic Process, Appl, vol.40, pp.127-143, 1992.
DOI : 10.1016/0304-4149(92)90141-c
URL : http://doi.org/10.1016/0304-4149(92)90141-c

Y. Lu and J. Garrido, Doubly periodic non-homogeneous Poisson models for hurricane data, Statistical Methodology, vol.2, issue.1, pp.17-35, 2005.
DOI : 10.1016/j.stamet.2004.10.004

Y. Lu and S. Li, On the probability of ruin in a Markov-modulated risk model, Insurance: Mathematics and Economics, vol.37, issue.3, pp.522-532, 2005.
DOI : 10.1016/j.insmatheco.2005.05.006

K. S. Meier-hellstern, A fitting algorithm for Markov-modulated poisson processes having two arrival rates, European Journal of Operational Research, vol.29, issue.3, pp.970-977, 1987.
DOI : 10.1016/0377-2217(87)90250-5

C. J. Neumann, B. R. Jarvinen, C. J. Mcadie, and J. D. Elms, Tropical Cyclones of the North Atlantic Ocean, Historical Climatology Series 6-2, National Climatic Data Center, pp.1871-1992, 1993.

A. Ng and H. Yang, On the joint distribution of surplus prior and immediately after ruin under a Markovian regime switching model, Stochastic Process, Appl, vol.116, pp.244-266, 2006.

E. Ohlsson and B. Johansson, Non-life insurance pricing with generalized linear models, 2010.
DOI : 10.1007/978-3-642-10791-7

F. Parisi and R. Lund, Seasonality and Return Periods of Landfalling Atlantic Basin Hurricanes, Australian <html_ent glyph="@amp;" ascii="&"/> New Zealand Journal of Statistics, vol.42, issue.3, pp.271-282, 2000.
DOI : 10.1111/1467-842X.00127

T. Rydén, Parameter estimation for Markov modulated poisson processes, Communications in Statistics. Stochastic Models, vol.73, issue.4, pp.795-829, 1994.
DOI : 10.1109/TPAMI.1984.4767581

T. Rydén, Consistent and Asymptotically Normal Parameter Estimates for Hidden Markov Models, The Annals of Statistics, vol.22, issue.4, pp.1884-1895, 1994.
DOI : 10.1214/aos/1176325762

T. Rydén, Consistent and asymptotically normal parameter estimates for Markov modulated Poisson processes, Scand, J. Stat, vol.22, pp.295-303, 1995.

T. Rydén, An EM algorithm for estimation in Markov-modulated Poisson processes, Computational Statistics & Data Analysis, vol.21, issue.4, pp.431-447, 1996.
DOI : 10.1016/0167-9473(95)00025-9

T. Rydén, On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions, Journal of Applied Probability, vol.9, issue.03, pp.640-653, 1996.
DOI : 10.1016/0025-5564(92)90023-P

P. Salvador, R. Valadas, and A. Pacheco, Multiscale fitting procedure using Markov modulated Poisson processes, Telecommunication Systems, vol.23, issue.1/2, pp.123-148, 2003.
DOI : 10.1023/A:1023672904130

S. L. Scott, Bayesian analysis of a two-state Markov modulated Poisson process, J. Comput . Graph. Statist, vol.8, pp.662-670, 1999.

H. J. Skaug, Markov Modulated Poisson Processes for Clustered Line Transect Data, Environmental and Ecological Statistics, vol.4, issue.2, pp.199-211, 2006.
DOI : 10.1007/s10651-005-0006-0

J. Vedani and F. Ramaharobandro, Continuous compliance: a proxy-based monitoring framework , preprint, available at https://hal.archives-ouvertes, p.866531, 2013.

A. Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Trans. Inform. Theory IT, pp.13-260, 1967.
DOI : 10.1109/tit.1967.1054010

J. Wei, H. Yang, and R. Wang, On the Markov-modulated insurance risk model with??tax, Bl??tter der DGVFM, vol.42, issue.1, pp.65-78, 2010.
DOI : 10.1007/s11857-010-0104-4

J. Zhu and H. Yang, Ruin theory for a Markov regime-switching model under a threshold dividend strategy, Insurance Math, Econom, vol.42, pp.311-318, 2008.