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Markov chain for transition probability.docx

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    http://en.wikipedia.org/wiki/File:Markovkate_01.svghttp://en.wikipedia.org/wiki/File:Markovkate_01.svghttp://en.wikipedia.org/wiki/File:Markovkate_01.svghttp://en.wikipedia.org/wiki/File:Markovkate_01.svghttp://en.wikipedia.org/wiki/Markov_chain#Finite_state_spacehttp://en.wikipedia.org/wiki/Markov_chain#Steady-state_analysis_and_the_time-inhomogeneous_Markov_chainhttp://en.wikipedia.org/wiki/Markov_chain#Steady-state_analysis_and_limiting_distributionshttp://en.wikipedia.org/wiki/Markov_chain#Ergodicityhttp://en.wikipedia.org/wiki/Markov_chain#Absorbing_stateshttp://en.wikipedia.org/wiki/Markov_chain#Expected_number_of_visitshttp://en.wikipedia.org/wiki/Markov_chain#Mean_recurrence_timehttp://en.wikipedia.org/wiki/Markov_chain#Recurrencehttp://en.wikipedia.org/wiki/Markov_chain#Periodicityhttp://en.wikipedia.org/wiki/Markov_chain#Reducibilityhttp://en.wikipedia.org/wiki/Markov_chain#Markov_chainshttp://en.wikipedia.org/wiki/Markov_chain#Examplehttp://en.wikipedia.org/wiki/Markov_chain#Variationshttp://en.wikipedia.org/wiki/Markov_chain#Formal_definitionhttp://en.wikipedia.org/wiki/Markov_chain#Introductionhttp://en.wikipedia.org/wiki/Statistical_modelinghttp://en.wikipedia.org/wiki/Markov_process#Markov_propertyhttp://en.wikipedia.org/wiki/Memorylessnesshttp://en.wikipedia.org/wiki/Stochastic_processhttp://en.wikipedia.org/wiki/Andrey_Markovhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-1http://en.wikipedia.org/wiki/Continuous-time_Markov_processhttp://en.wikipedia.org/wiki/Markov_chain#p-searchhttp://en.wikipedia.org/wiki/Markov_chain#mw-navigation
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    http://en.wikipedia.org/wiki/Markov_chain#External_linkshttp://en.wikipedia.org/wiki/Markov_chain#Referenceshttp://en.wikipedia.org/wiki/Markov_chain#Noteshttp://en.wikipedia.org/wiki/Markov_chain#See_alsohttp://en.wikipedia.org/wiki/Markov_chain#Historyhttp://en.wikipedia.org/wiki/Markov_chain#Fittinghttp://en.wikipedia.org/wiki/Markov_chain#Markov_text_generatorshttp://en.wikipedia.org/wiki/Markov_chain#Baseballhttp://en.wikipedia.org/wiki/Markov_chain#Musichttp://en.wikipedia.org/wiki/Markov_chain#Gameshttp://en.wikipedia.org/wiki/Markov_chain#Geneticshttp://en.wikipedia.org/wiki/Markov_chain#Mathematical_biologyhttp://en.wikipedia.org/wiki/Markov_chain#Social_scienceshttp://en.wikipedia.org/wiki/Markov_chain#Economics_and_financehttp://en.wikipedia.org/wiki/Markov_chain#Statisticshttp://en.wikipedia.org/wiki/Markov_chain#Internet_applicationshttp://en.wikipedia.org/wiki/Markov_chain#Queueing_theoryhttp://en.wikipedia.org/wiki/Markov_chain#Information_scienceshttp://en.wikipedia.org/wiki/Markov_chain#Testinghttp://en.wikipedia.org/wiki/Markov_chain#Chemistryhttp://en.wikipedia.org/wiki/Markov_chain#Physicshttp://en.wikipedia.org/wiki/Markov_chain#Applicationshttp://en.wikipedia.org/wiki/Markov_chain#Locally_interacting_Markov_chainshttp://en.wikipedia.org/wiki/Markov_chain#General_state_spacehttp://en.wikipedia.org/wiki/Markov_chain#Bernoulli_schemehttp://en.wikipedia.org/wiki/Markov_chain#Reversible_Markov_chainhttp://en.wikipedia.org/wiki/Markov_chain#Convergence_speed_to_the_stationary_distributionhttp://en.wikipedia.org/wiki/Markov_chain#Time-homogeneous_Markov_chain_with_a_finite_state_space
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    http://en.wikipedia.org/wiki/File:AAMarkov.jpghttp://en.wikipedia.org/wiki/File:AAMarkov.jpghttp://en.wikipedia.org/wiki/File:AAMarkov.jpghttp://en.wikipedia.org/wiki/File:AAMarkov.jpghttp://en.wikipedia.org/wiki/Conditional_probability_distributionhttp://en.wikipedia.org/wiki/Natural_numbershttp://en.wikipedia.org/wiki/Integershttp://en.wikipedia.org/wiki/Markov_chain_Monte_Carlohttp://en.wikipedia.org/wiki/Markov_chain#cite_note-3http://en.wikipedia.org/wiki/Markov_chain#cite_note-3http://en.wikipedia.org/wiki/Continuous-time_Markov_processhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-2http://en.wikipedia.org/wiki/Discrete-timehttp://en.wikipedia.org/wiki/State-spacehttp://en.wikipedia.org/wiki/Markov_processhttp://en.wikipedia.org/wiki/Markov_propertyhttp://en.wikipedia.org/wiki/Stochastic_processhttp://en.wikipedia.org/wiki/Andrey_Markov
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    http://en.wikipedia.org/wiki/Continuous-time_Markov_processhttp://en.wikipedia.org/wiki/Directed_graphhttp://en.wikipedia.org/wiki/Countable_sethttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Examples_of_Markov_chainshttp://en.wikipedia.org/wiki/Number_linehttp://en.wikipedia.org/wiki/Random_walk
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    http://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/File:MarkovChain1.pnghttp://en.wikipedia.org/wiki/Transition_matrixhttp://en.wikipedia.org/wiki/Recessionhttp://en.wikipedia.org/wiki/Market_trend#Bear_markethttp://en.wikipedia.org/wiki/Market_trend#Bull_markethttp://en.wikipedia.org/wiki/Wikipedia:Please_clarifyhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-5http://en.wikipedia.org/wiki/Additive_Markov_chain
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    http://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variableshttp://en.wikipedia.org/wiki/Finite_state_machinehttp://en.wikipedia.org/wiki/Markov_chain#cite_note-CTCN-7http://en.wikipedia.org/wiki/Markov_chain#cite_note-MCSS-6http://en.wikipedia.org/wiki/Stochastic_row_vector
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    http://en.wikipedia.org/wiki/Exponenthttp://en.wikipedia.org/wiki/Indexed_familyhttp://en.wikipedia.org/wiki/Marginal_distributionhttp://en.wikipedia.org/wiki/Chapman%E2%80%93Kolmogorov_equation
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    http://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Bipartite_graphhttp://en.wikipedia.org/wiki/Greatest_common_divisorhttp://en.wikipedia.org/wiki/Periodic_functionhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-8http://en.wikipedia.org/wiki/Equivalence_classeshttp://en.wikipedia.org/wiki/Equivalence_relation
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    http://en.wikipedia.org/wiki/Ergodic_theoryhttp://en.wikipedia.org/wiki/Absorbing_Markov_chainhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/Expected_value
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    http://en.wikipedia.org/wiki/Markov_chain#Reducibilityhttp://en.wikipedia.org/wiki/Invariant_measure
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    http://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theoremhttp://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theoremhttp://en.wikipedia.org/wiki/Simplexhttp://en.wikipedia.org/wiki/Eigenvaluehttp://en.wikipedia.org/wiki/Eigenvector
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    http://en.wikipedia.org/wiki/Eigendecompositionhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-9http://en.wikipedia.org/wiki/Stochastic_matrixhttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Fact_and_Reference_Checkhttp://en.wikipedia.org/wiki/Wikipedia:Citing_sources#Inline_citationshttp://en.wikipedia.org/wiki/Wikipedia:External_linkshttp://en.wikipedia.org/wiki/Wikipedia:Citing_sourceshttp://en.wikipedia.org/wiki/Stochastic_matrixhttp://en.wikipedia.org/wiki/System_of_linear_equationshttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Stochastic_matrixhttp://en.wikipedia.org/wiki/Stochastic_matrixhttp://en.wikipedia.org/wiki/Zero_matrixhttp://en.wikipedia.org/wiki/Identity_matrix
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    http://en.wikipedia.org/wiki/Detailed_balancehttp://en.wikipedia.org/wiki/Markov_chain#cite_note-11http://en.wikipedia.org/wiki/Markov_chain#cite_note-10http://en.wikipedia.org/wiki/Orthonormal
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    http://en.wikipedia.org/wiki/Harris_chainhttp://en.wikipedia.org/wiki/Bernoulli_processhttp://en.wikipedia.org/wiki/Bernoulli_schemehttp://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo
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    http://en.wikipedia.org/wiki/File:Simple_mechanism.svghttp://en.wikipedia.org/wiki/File:Simple_mechanism.svghttp://en.wikipedia.org/wiki/File:Question_book-new.svghttp://en.wikipedia.org/wiki/File:Simple_mechanism.svghttp://en.wikipedia.org/wiki/File:Simple_mechanism.svghttp://en.wikipedia.org/wiki/File:Question_book-new.svghttp://en.wikipedia.org/wiki/File:Simple_mechanism.svghttp://en.wikipedia.org/wiki/File:Simple_mechanism.svghttp://en.wikipedia.org/wiki/File:Question_book-new.svghttp://en.wikipedia.org/wiki/Michaelis-Menten_kineticshttp://en.wikipedia.org/wiki/Michaelis-Menten_kineticshttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Statistical_mechanicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidencehttp://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Wikipedia:Verifiabilityhttp://en.wikipedia.org/wiki/Wikipedia:Citing_sourceshttp://en.wikipedia.org/wiki/Markov_chain#cite_note-13http://en.wikipedia.org/wiki/Markov_chain#cite_note-12http://en.wikipedia.org/w/index.php?title=Stochastic_cellular_automata&action=edit&redlink=1http://en.wikipedia.org/wiki/Interacting_particle_systemhttp://en.wikipedia.org/w/index.php?title=Locally_interacting_Markov_chains&action=edit&redlink=1http://en.wikipedia.org/wiki/Harris_chainhttp://en.wikipedia.org/wiki/Harris_chain
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    http://en.wikipedia.org/wiki/Markov_chain#cite_note-MacTutor_Biography.7Cid.3DErlang-16http://en.wikipedia.org/wiki/Agner_Krarup_Erlanghttp://en.wikipedia.org/wiki/Agner_Krarup_Erlanghttp://en.wikipedia.org/wiki/Queueing_theoryhttp://en.wikipedia.org/wiki/Bioinformaticshttp://en.wikipedia.org/wiki/Viterbi_algorithmhttp://en.wikipedia.org/wiki/Hidden_Markov_Modelshttp://en.wikipedia.org/wiki/Reinforcement_learninghttp://en.wikipedia.org/wiki/Pattern_recognitionhttp://en.wikipedia.org/wiki/State_estimationhttp://en.wikipedia.org/wiki/Arithmetic_codinghttp://en.wikipedia.org/wiki/Entropy_encodinghttp://en.wikipedia.org/wiki/Data_compressionhttp://en.wikipedia.org/wiki/Information_entropyhttp://en.wikipedia.org/wiki/Information_theoryhttp://en.wikipedia.org/wiki/A_mathematical_theory_of_communicationhttp://en.wikipedia.org/wiki/Claude_Shannonhttp://en.wikipedia.org/wiki/Markov_blankethttp://en.wikipedia.org/wiki/Markov_chain#cite_note-15http://en.wikipedia.org/wiki/Superlatticehttp://en.wikipedia.org/wiki/Steric_effectshttp://en.wikipedia.org/wiki/Copolymerhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-14
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    http://en.wikipedia.org/wiki/Probability_vectorhttp://en.wikipedia.org/wiki/SuperColliderhttp://en.wikipedia.org/wiki/Max_%28software%29http://en.wikipedia.org/wiki/CSoundhttp://en.wikipedia.org/wiki/Softwarehttp://en.wikipedia.org/wiki/Algorithmic_compositionhttp://en.wikipedia.org/wiki/Hi_Ho%21_Cherry-Ohttp://en.wikipedia.org/wiki/Snakes_and_Laddershttp://en.wikipedia.org/wiki/Snakes_and_Laddershttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Motoo_Kimurahttp://en.wikipedia.org/wiki/Diffusion_equationhttp://en.wikipedia.org/wiki/Genetic_drifthttp://en.wikipedia.org/wiki/Population_geneticshttp://en.wikipedia.org/wiki/Markov_chain#cite_note-25http://en.wikipedia.org/wiki/Ion_channelhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-24http://en.wikipedia.org/wiki/Epithelial_cellshttp://en.wikipedia.org/wiki/Leslie_matrixhttp://en.wikipedia.org/wiki/Population_processhttp://en.wikipedia.org/wiki/Population_processhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-23http://en.wikipedia.org/wiki/Democratichttp://en.wikipedia.org/wiki/Authoritarianhttp://en.wikipedia.org/wiki/Politicalhttp://en.wikipedia.org/wiki/Bourgeoisiehttp://en.wikipedia.org/wiki/Capitalismhttp://en.wikipedia.org/wiki/Economic_developmenthttp://en.wikipedia.org/wiki/Das_Kapitalhttp://en.wikipedia.org/wiki/Karl_Marxhttp://en.wikipedia.org/wiki/Path-dependenthttp://en.wikipedia.org/wiki/Markov_chain#cite_note-22http://en.wikipedia.org/wiki/General_equilibrium
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    http://en.wikipedia.org/wiki/Markov_chain#cite_note-31http://en.wikipedia.org/wiki/Markov_chain#cite_note-30http://en.wikipedia.org/wiki/Markov_chain#cite_note-29http://en.wikipedia.org/wiki/Markov_chain#cite_note-28http://en.wikipedia.org/wiki/Markov_chain#cite_note-Roads-27http://en.wikipedia.org/wiki/Phrase_%28music%29http://en.wikipedia.org/wiki/Markov_chain#cite_note-26http://en.wikipedia.org/wiki/Hertzhttp://en.wikipedia.org/wiki/MIDI
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    http://en.wikipedia.org/wiki/Variable-order_Markov_modelhttp://en.wikipedia.org/wiki/Semi-Markov_processhttp://en.wikipedia.org/wiki/Markov_blankethttp://en.wikipedia.org/wiki/Markov_networkhttp://en.wikipedia.org/wiki/Markov_chain_Monte_Carlohttp://en.wikipedia.org/wiki/Markov_information_sourcehttp://en.wikipedia.org/wiki/Markov_processhttp://en.wikipedia.org/wiki/Quantum_Markov_chainhttp://en.wikipedia.org/wiki/Markov_chain_geostatisticshttp://en.wikipedia.org/wiki/Markov_chain_mixing_timehttp://en.wikipedia.org/wiki/Telescoping_Markov_chainhttp://en.wikipedia.org/wiki/Hidden_Markov_modelhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-38http://en.wikipedia.org/wiki/Markov_chain#cite_note-37http://en.wikipedia.org/wiki/Markov_chain#cite_note-MacTutor_Biography.7Cid.3DErlang-16http://en.wikipedia.org/wiki/Agner_Krarup_Erlanghttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Eugene_Oneginhttp://en.wikipedia.org/wiki/Law_of_large_numbershttp://en.wikipedia.org/wiki/Ergodic_hypothesishttp://en.wikipedia.org/wiki/Brownian_motionhttp://en.wikipedia.org/wiki/Andrey_Nikolaevich_Kolmogorovhttp://en.wikipedia.org/wiki/Andrey_Markovhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-36http://en.wikipedia.org/wiki/Spam_filterhttp://en.wikipedia.org/wiki/Spam_in_blogshttp://en.wikipedia.org/wiki/Unsolicited_emailhttp://en.wikipedia.org/wiki/E-mail_spamhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-Hartman-35http://en.wikipedia.org/wiki/Mark_V_Shaneyhttp://en.wikipedia.org/wiki/Mark_V_Shaneyhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-33http://en.wikipedia.org/wiki/Dissociated_presshttp://en.wikipedia.org/wiki/Dissociated_presshttp://en.wikipedia.org/wiki/Parody_generatorhttp://en.wikipedia.org/wiki/Markov_chain#cite_note-32http://en.wikipedia.org/wiki/Astroturfhttp://en.wikipedia.org/wiki/Base_stealinghttp://en.wikipedia.org/wiki/Bunt_%28baseball%29
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    http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1768http://en.wikipedia.org/wiki/Markov_chain#cite_ref-pagerank_18-0http://www.google.com/patents?vid=6285999http://en.wikipedia.org/wiki/Markov_chain#cite_ref-17http://en.wikipedia.org/wiki/University_of_St_Andrewshttp://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_archivehttp://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_archivehttp://www-history.mcs.st-andrews.ac.uk/Biographies/Erlang.htmlhttp://en.wikipedia.org/wiki/Edmund_F._Robertsonhttp://en.wikipedia.org/wiki/John_J._O%27Connor_%28mathematician%29http://en.wikipedia.org/wiki/Markov_chain#cite_ref-MacTutor_Biography.7Cid.3DErlang_16-1http://en.wikipedia.org/wiki/Markov_chain#cite_ref-MacTutor_Biography.7Cid.3DErlang_16-0http://en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1107.2FS0108767311044874&action=edit&editintro=Template:Cite_doi/editintro2http://dx.doi.org/10.1107%2FS0108767311044874http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-15http://www.ncbi.nlm.nih.gov/pubmed/19527020http://en.wikipedia.org/wiki/PubMed_Identifierhttp://dx.doi.org/10.1021%2Fci9000458http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-14http://books.google.nl/books?id=0Wa7AAAAIAAJ&pg=PA181&lpg=PA181&dq=locally+interacting+markov+chains+toom+Dobrushin&source=bl&ots=iKVIdep5R9&sig=jIz_HNJPuFnq21xxrH_fmXxXlew&hl=en&sa=X&ei=63m7UITZN6eb1AXGtYGAAQ&sqi=2&redir_esc=y#v=onepage&q=locally%20interacting%20markov%20chains%20toom%20Dobrushin&f=falsehttp://books.google.nl/books?id=0Wa7AAAAIAAJ&pg=PA181&lpg=PA181&dq=locally+interacting+markov+chains+toom+Dobrushin&source=bl&ots=iKVIdep5R9&sig=jIz_HNJPuFnq21xxrH_fmXxXlew&hl=en&sa=X&ei=63m7UITZN6eb1AXGtYGAAQ&sqi=2&redir_esc=y#v=onepage&q=locally%20interacting%20markov%20chains%20toom%20Dobrushin&f=falsehttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-13http://dx.doi.org/10.1016/0001-8708%2870%2990034-4http://en.wikipedia.org/wiki/Markov_chain#cite_ref-12http://dx.doi.org/10.1103%2FPhysRevE.84.041112http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-11http://en.wikipedia.org/wiki/Markov_chain#cite_ref-10http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.6191http://en.wikipedia.org/wiki/Markov_chain#cite_ref-9http://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-4739-8http://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-4739-8http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://books.google.co.uk/books?id=6Cg5Nq5sSv4C&lpg=PA16&dq=essential%20class%20markov&pg=PA16#v=onepagehttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-8http://decision.csl.uiuc.edu/~meyn/pages/CTCN/CTCN.htmlhttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-CTCN_7-1http://en.wikipedia.org/wiki/Markov_chain#cite_ref-CTCN_7-0https://netfiles.uiuc.edu/meyn/www/spm_files/book.htmlhttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-MCSS_6-0http://en.wikipedia.org/wiki/Special:BookSources/9781904868743http://en.wikipedia.org/wiki/Markov_chain#cite_ref-5http://en.wikipedia.org/wiki/Special:BookSources/0199206139http://en.wikipedia.org/wiki/Special:BookSources/0199206139http://en.wikipedia.org/wiki/Markov_chain#cite_ref-4http://en.wikipedia.org/wiki/Special:BookSources/0816266646http://en.wikipedia.org/wiki/Markov_chain#cite_ref-3http://en.wikipedia.org/wiki/Special:BookSources/052181099Xhttp://en.wikipedia.org/wiki/Special:BookSources/052181099Xhttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-2http://www.statslab.cam.ac.uk/~james/Markov/http://en.wikipedia.org/wiki/James_R._Norrishttp://en.wikipedia.org/wiki/Markov_chain#cite_ref-1http://en.wikipedia.org/wiki/Markov_decision_process
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