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@book{dobrow2016introduction,
  title =        {Introduction to Stochastic Processes with R},
  author =       {Dobrow, Robert P},
  year =         {2016},
  publisher =    {John Wiley \& Sons}
}

@manual{pkg:ctmcd,
  title =        {ctmcd: Estimating the Parameters of a
                  Continuous-Time Markov Chain from Discrete-Time
                  Data},
  author =       {Marius Pfeuffer},
  year =         {2017},
  note =         {R package version 1.1},
  url =          {https://CRAN.R-project.org/package=ctmcd}
}


@article{Hu2002,
  author =       {Hu, Yen Ting and Kiesel, Rudiger and Perraudin,
                  William},
  doi =          {10.1016/S0378-4266(02)00268-6},
  isbn =         {0378-4266},
  issn =         {03784266},
  journal =      {Journal of Banking and Finance},
  keywords =     {Credit rating,Credit risk,Ordered probit,Sovereign
                  default},
  number =       {7},
  pages =        {1383--1406},
  title =        {{The estimation of transition matrices for sovereign
                  credit ratings}},
  volume =       {26},
  year =         {2002}
}

@book{de2016assicurazioni,
  title =        {Assicurazioni sulla salute: caratteristiche, modelli
                  attuariali e basi tecniche},
  author =       {{De Angelis, Paolo} and {Di Falco, L.}},
  isbn =         {9788815260840},
  series =       {Il Mulino},
  url =          {https://books.google.it/books?id=D56bjgEACAAJ},
  year =         {2016},
  publisher =    {Il Mulino}
}

@mastersthesis{skuriat2005statistical,
  author =       "Skuriat-Olechnowska, Monika",
  title =        "Statistical inference and hypothesis testing for
                  Markov chains with Interval Censoring",
  school =       "TUDelft",
  year =         "2005"
}

@article{kullback1962tests,
  title =        {Tests for Contingency Tables and Marltov Chains},
  author =       {Kullback, S and Kupperman, Michael and Ku, HH},
  journal =      {Technometrics},
  volume =       {4},
  number =       {4},
  pages =        {573--608},
  year =         {1962},
  publisher =    {Taylor \& Francis}
}

@article{israel2001finding,
  title =        {Finding generators for Markov chains via empirical
                  transition matrices, with applications to credit
                  ratings},
  author =       {Israel, Robert B and Rosenthal, Jeffrey S and Wei,
                  Jason Z},
  journal =      {Mathematical finance},
  volume =       {11},
  number =       {2},
  pages =        {245--265},
  year =         {2001},
  publisher =    {Wiley Online Library}
}

@manual{pkg:RcppParallel,
  title =        {RcppParallel: Parallel Programming Tools for 'Rcpp'},
  author =       {JJ Allaire and Romain Francois and Kevin Ushey and
                  Gregory Vandenbrouck and Marcus Geelnard and
                  {Intel}},
  year =         {2016},
  note =         {R package version 4.3.19},
  url =          {https://rcppcore.github.io/RcppParallel/}
}

@manual{pkg:MultinomialCI,
  title =        {MultinomialCI: Simultaneous confidence intervals for
                  multinomial proportions according to the method by
                  Sison and Glaz},
  author =       {Pablo J. Villacorta},
  year =         {2012},
  note =         {R package version 1.0},
  url =          {https://CRAN.R-project.org/package=MultinomialCI}
}

@article{sison1995simultaneous,
  title =        {Simultaneous confidence intervals and sample size
                  determination for multinomial proportions},
  author =       {Sison, Cristina P and Glaz, Joseph},
  journal =      {Journal of the American Statistical Association},
  volume =       {90},
  number =       {429},
  pages =        {366--369},
  year =         {1995},
  publisher =    {Taylor \& Francis}
}

@article{konstantopoulos2009markov,
  title =        {Markov Chains and Random Walks},
  author =       {Konstantopoulos, Takis},
  journal =      {Lecture notes},
  year =         {2009}
}

@article{craigSendi,
  author =       {{B. A. Craig} and {A. A. Sendi}},
  title =        {Estimation of the Transition Matrix of a
                  Discrete-Time Markov Chain},
  journal =      {Health Economics},
  year =         {2002},
  volume =       {11},
  pages =        {33--42}
}

@misc{bardPpt,
  author =       {J. F. Bard},
  title =        {Lecture 12.5 - Additional Issues Concerning
                  Discrete-Time Markov Chains},
  month =        {April},
  year =         {2000},
  url ={https://www.me.utexas.edu/~jensen%20/ORMM/instruction/powerpoint/or_models_09/12.5_dtmc2.ppt}
}

@incollection{bremaud1999discrete,
  author =       {Br{\'e}maud, Pierre},
  title =        {Discrete-Time Markov Models},
  booktitle =    {Markov Chains},
  publisher =    {Springer},
  year =         {1999},
  pages =        {53--93}
}

@book{chambers,
  title =        {Software for Data Analysis: Programming with
                  \proglang{R}},
  publisher =    {Springer-Verlag},
  year =         {2008},
  author =       {Chambers, J.M.},
  series =       {Statistics and computing},
  isbn =         {9780387759357},
  lccn =         {2008922937}
}

@book{ching2006markov,
  title =        {Markov Chains: Models, Algorithms and Applications},
  publisher =    {Springer-Verlag},
  year =         {2006},
  author =       {Ching, W.K. and Ng, M.K.},
  series =       {International Series in Operations Research \&
                  Management Science},
  isbn =         {9780387293356},
  lccn =         {2005933263}
}

@article{pkg:igraph,
  author =       {Gabor Csardi and Tamas Nepusz},
  title =        {The \pkg{igraph} Software Package for Complex
                  Network Research},
  journal =      {InterJournal},
  year =         {2006},
  volume =       {Complex Systems},
  pages =        {1695},
  url =          {https://igraph.sourceforge.net/}
}

@book{denuit2007actuarial,
  title =        {Actuarial modelling of claim counts: Risk
                  classification, credibility and bonus-malus systems},
  publisher =    {Wiley},
  year =         {2007},
  author =       {Denuit, Michel and Mar{\'e}chal, Xavier and
                  Pitrebois, Sandra and Walhin, Jean-Fran{\c{c}}ois}
}

@book{deshmukh2012multiple,
  title =        {Multiple Decrement Models in Insurance: An
                  Introduction Using \proglang{R}},
  publisher =    {Springer-Verlag},
  year =         {2012},
  author =       {Deshmukh, S.R.},
  series =       {SpringerLink : B{\"u}cher},
  isbn =         {9788132206590},
  lccn =         {2012942476}
}

@book{RcppR,
  title =        {Seamless \proglang{R} and \proglang{C++} Integration
                  with \pkg{Rcpp}},
  publisher =    {Springer-Verlag},
  year =         {2013},
  author =       {Dirk Eddelbuettel},
  address =      {New York},
  note =         {ISBN 978-1-4614-6867-7}
}

@misc{renaldoMatlab,
  author =       {Renaldo Feres},
  title =        {Notes for Math 450 \proglang{MATLAB} Listings for
                  Markov Chains},
  year =         {2007},
  url =          {https://www.math.wustl.edu/~feres/Math450Lect04.pdf}
}

@manual{mcmcR,
  title =        {mcmc: Markov Chain Monte Carlo},
  author =       {Charles J. Geyer and Leif T. Johnson},
  year =         {2013},
  note =         {\proglang{R} package version 0.9-2},
  url =          {https://CRAN.R-project.org/package=mcmc}
}

@incollection{glassHall,
  author =       {Glass, D.V. and Hall, J. R.},
  title =        {Social Mobility in Great Britain: A Study in
                  Intergenerational Change in Status},
  booktitle =    {Social Mobility in Great Britain},
  publisher =    {Routledge and Kegan Paul},
  year =         {1954}
}

@manual{expmR,
  title =        {\pkg{expm}: Matrix Exponential},
  author =       {Vincent Goulet and Christophe Dutang and Martin
                  Maechler and David Firth and Marina Shapira and
                  Michael Stadelmann and
                  {expm-developers@lists.R-forge.R-project.org}},
  year =         {2013},
  note =         {R package version 0.99-1},
  url =          {https://CRAN.R-project.org/package=expm}
}

@manual{hmmR,
  title =        {\pkg{HMM}: HMM - Hidden Markov Models},
  author =       {Scientific Software Development - Dr. Lin Himmelmann
                  and {www.linhi.com}},
  year =         {2010},
  note =         {\proglang{R} package version 1.0},
  url =          {https://CRAN.R-project.org/package=HMM}
}

@book{landOfOz,
  title =        {Introduction to Finite Mathematics},
  publisher =    {Prentice Hall},
  year =         {1974},
  author =       {{J. G. Kemeny} and {J. L.Snell} and
                  {G. L. Thompson}}
}

@article{msmR,
  author =       {Christopher H. Jackson},
  title =        {Multi-State Models for Panel Data: The \pkg{msm}
                  Package for \proglang{R}},
  journal =      {Journal of Statistical Software},
  year =         {2011},
  volume =       {38},
  pages =        {1--29},
  number =       {8},
  url =          {https://www.jstatsoft.org/v38/i08/}
}

@misc{manchesterR,
  author =       {Ian Jacob},
  month =        {May},
  year =         {2014},
  title =        {Is R Cost Effective?},
  language =     {En},
  howpublished = {Electronic},
  organization = {Manchester Centre for Health Economics},
  note =         {Presented on Manchester R Meeting}
}

@TECHREPORT{blandenEtAlii,
  author =       {Jo Blanden, Paul Gregg and Stephen Machin},
  title =        {Intergenerational Mobility in Europe and North
                  America},
  institution =  {Center for Economic Performances},
  year =         {2005},
  owner =        {Giorgio Copia},
  timestamp =    {2014.01.01},
  url ={https://cep.lse.ac.uk/about/news/IntergenerationalMobility.pdf}
}

@misc{Konstantopoulos2009,
  author =       {Konstantopoulos, Takis},
  title =        {Markov Chains and Random Walks},
  year =         {2009},
  url =          {https://www2.math.uu.se/~takis/public_html/McRw/mcrw.pdf}
}

@misc{montgomery,
  author =       {James Montgomery},
  title =        {Communication Classes},
  year =         {2009},
  url =          {https://www.ssc.wisc.edu/~jmontgom/commclasses.pdf}
}

@manual{DTMCPackR,
  title =        {\pkg{DTMCPack}: Suite of Functions Related to
                  Discrete-Time Discrete-State Markov Chains},
  author =       {William Nicholson},
  year =         {2013},
  note =         {R package version 0.1-2},
  url =          {https://CRAN.R-project.org/package=DTMCPack}
}

@article{averyHenderson,
  author =       {{P. J. Avery} and {D. A. Henderson}},
  title =        {Fitting Markov Chain Models to Discrete State
                  Series},
  journal =      {Applied Statistics},
  year =         {1999},
  volume =       {48},
  pages =        {53-61},
  number =       {1}
}

@manual{rSoftware,
  title =        {\proglang{R}: A Language and Environment for
                  Statistical Computing},
  author =       {{R Core Team}},
  organization = {R Foundation for Statistical Computing},
  address =      {Vienna, Austria},
  year =         {2013},
  url =          {https://www.R-project.org/}
}

@manual{pkg:matlab,
  title =        {\pkg{matlab}: \proglang{MATLAB} emulation package},
  author =       {P. Roebuck},
  year =         {2011},
  note =         {R package version 0.8.9},
  url =          {https://CRAN.R-project.org/package=matlab}
}

@misc{probBook,
  author =       {Laurie Snell},
  title =        {Probability Book: chapter 11},
  year =         {1999},
  url =          {https://web.archive.org/web/20150721052835/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf}
}

@article{pkg:markovchain,
  author =       {Giorgio Alfredo Spedicato},
  title =        {{Discrete Time Markov Chains with R}},
  year =         {2017},
  journal =      {{The R Journal}},
  url =
                  {https://journal.r-project.org/articles/RJ-2017-036/index.html}
}


@manual{MAPmcR,
  title =        {Bayesian Inference of First Order Markov Chains},
  author =       {Sai Bhargav Yalamanchi and Giorgio Alfredo
                  Spedicato},
  month =        {06},
  year =         {2015},
  note =         {R package version 0.2.5}
}

@misc{wiki:markov,
  author =       {Wikipedia},
  title =        {Markov chain --- Wikipedia{,} The Free Encyclopedia},
  year =         {2013},
  note =         {[Online; accessed 23-August-2013]},
  url =
                 {https://en.wikipedia.org/w/index.php?title=Markov_chain&oldid=568910294}
}

@manual{CreditMetricsR,
  title =        {CreditMetrics: Functions for Calculating the
                  CreditMetrics Risk Model},
  author =       {Andreas Wittmann},
  year =         {2007},
  note =         {\proglang{R} package version 0.0-2}
}

@manual{mathematica9,
  title =        {\proglang{Mathematica}},
  author =       {Wolfram Research, Inc.},
  organization = {Wolfram Research, Inc.},
  edition =      {ninth},
  year =         {2013},
  adddress =     {Champaign, Illinois}
}

@misc{mathematica9MarkovChain,
  author =       {Wolfram Research, Inc.},
  year =         {2013},
  organization = {Wolfram Research, Inc.},
  url ={https://www.wolfram.com/mathematica/new-in-9/markov-chains-and-queues/structural-properties-of-finite-markov-processes.html}
}

@article{sch,
  author =       {Christopher C. Strelioff and James P. Crutchfield
                  and Alfred W. Hubler},
  title =        {Inferring Markov Chains: Bayesian Estimation, Model
                  Comparison, Entropy Rate, and Out-of-class Modeling},
  journal =      {Sante Fe Working Papers},
  year =         {2007},
  url =          {https://arxiv.org/abs/math/0703715/}
}

@article{mstateR,
  author =       {Liesbeth C. de Wreede and Marta Fiocco and Hein
                  Putter},
  title =        {\pkg{mstate}: An \proglang{R} Package for the
                  Analysis of Competing Risks and Multi-State Models},
  journal =      {Journal of Statistical Software},
  year =         {2011},
  volume =       {38},
  pages =        {1--30},
  number =       {7},
  url =          {https://www.jstatsoft.org/v38/i07/}
}

@mastersthesis{MSkuriat,
  author =       {Monika Skuriat-Olechnowska},
  title =        {Statistical inference and hypothesis testing for
                  Markov chains with Interval Censoring},
  school =       {Delft University of Technology},
  type =         {diploma thesis},
  year =         {2005}
}

@misc{wiki:CI,
  author =       {Wikipedia},
  title =        {Confidence interval --- Wikipedia{,} The Free
                  Encyclopedia},
  year =         {2015},
  url =
                  {https://en.wikipedia.org/w/index.php?title=Confidence_interval&oldid=667353161},
  note =         {[Online; accessed 21-June-2015]}
}

@book{pardo2005statistical,
  title =        {Statistical inference based on divergence measures},
  author =       {Pardo, Leandro},
  year =         {2005},
  publisher =    {CRC Press}
}

@article{anderson1957statistical,
  title =        {Statistical inference about Markov chains},
  author =       {Anderson, Theodore W and Goodman, Leo A},
  journal =      {The Annals of Mathematical Statistics},
  pages =        {89--110},
  year =         {1957},
  publisher =    {JSTOR}
}

@article{ching2008higher,
  title =        {Higher-order multivariate Markov chains and their
                  applications},
  author =       {Ching, Wai-Ki and Ng, Michael K and Fung, Eric S},
  journal =      {Linear Algebra and its Applications},
  volume =       {428},
  number =       {2},
  pages =        {492--507},
  year =         {2008},
  publisher =    {Elsevier}
}

@incollection{ching2013higher,
  title =        {Higher-order markov chains},
  author =       {Ching, Wai-Ki and Huang, Ximin and Ng, Michael K and
                  Siu, Tak-Kuen},
  booktitle =    {Markov Chains},
  pages =        {141--176},
  year =         {2013},
  publisher =    {Springer}
}

@manual{pkg:Rsolnp,
  title =        {Rsolnp: General Non-linear Optimization Using
                  Augmented Lagrange Multiplier Method},
  author =       {Alexios Ghalanos and Stefan Theussl},
  year =         {2014},
  note =         {R package version 1.15.}
}
  
@PhdThesis{YinyuYe,
  title =        {Interior Algorithms for Linear, Quadratic, and
                  Linearly Constrained Non-Linear Programming},
  author =       {Yinyu Ye},
  year =         {1987},
  school =       {Department of {ESS}, Stanford University}
}

@book{NorrisBook,
  title =        {Markovchains},
  author =       {J. R. Norris},
  year =         {1998},
  publisher =    {Cambridge University Press}
}

@article{ictmcpaper,
  author    = {Thomas Krak, Jasper De Bock, Arno Siebes},
  title     = {Imprecise Continuous Time Markov Chains},
  journal   = {International Journal of Approximate Reasoning},
  year      = {2017},
  volume    = {88},
  pages     = {452-528},
  publisher = {arXiv}
}

@misc{committorlink,
  author =       {StackOverflow},
  url =
                  {https://math.stackexchange.com/questions/1450399/probability-that-a-chain-will-enter-state-5-before-it-enters-state-3?newreg=82f90b66b949495a91661caad24db915},
  year =         {2015}
}

@book{GallagerBook,
  title =        {Stochastic Processes: Theory for Applications},
  author =       {Robert G. Gallager},
  year =         {2013},
  publisher =    {Cambridge University Press}
}

@misc{Sigman,
  title =        {Continuous Time markovchains},
  author =       {Karl Sigman},
  year =         {2009},
  publisher =    {Columbia University}
}

@article{freqArticle,
  author    = {Alexander Kreinin, Marina Sidelnikova},
  title     = {Regularization Algorithms for Transition Matrices},
  journal   = {Algo Research Quarterly},
  year      = {2001},
  volume    = {4},
  number    = {1/2},
  pages     = {23--40},
  month     = mar,
  publisher = {ALGO RESEARCH QUARTERLY}
}

@book{GrinsteadSnell,
    author = {Grinstead, Charles M. and Snell, Laurie J.},
    booktitle = {Introduction to Probability},
    edition = {Version dated 4 July 2006},
    publisher = {American Mathematical Society},
    title = {{Grinstead and Snell's Introduction to Probability}},
    url = {https://math.dartmouth.edu/~prob/prob/prob.pdf},
    year = {2006}
}

@article{noe_constructing_2009,
	title = {Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations},
	volume = {106},
	copyright = {© 2009 .  Freely available online through the PNAS open access option.},
	issn = {0027-8424, 1091-6490},
	url = {https://www.pnas.org/content/106/45/19011},
	doi = {10.1073/pnas.0905466106},
	language = {en},
	number = {45},
	urldate = {2019-01-13},
	journal = {Proceedings of the National Academy of Sciences},
	author = {Noé, Frank and Schütte, Christof and Vanden-Eijnden, Eric and Reich, Lothar and Weikl, Thomas R.},
	month = nov,
	year = {2009},
	pmid = {19887634},
	keywords = {committor},
	pages = {19011--19016}
}

@article{Tarjan,
  doi = {10.1137/0201010},
  url = {https://doi.org/10.1137/0201010},
  year = {1972},
  month = jun,
  publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
  volume = {1},
  number = {2},
  pages = {146--160},
  author = {Robert Tarjan},
  title = {Depth-First Search and Linear Graph Algorithms},
  journal = {{SIAM} Journal on Computing}
}
