{"doi":"10.2174/9789815080476123010009","title":"Markov Chain Process","abstract":"<jats:p>In this chapter, and from the historical introduction raised in the previous chapters, we introduce and exemplify all the components of a Markov Chain\nProcess such as: initial state vector, Markov property (or Markov property), matrix of transition probabilities, and steady-state vector. A Markov Chain Process\nis formally defined and by way of categorization this process is divided into two\ntypes: Discrete-Time Markov Chain Process and Continuous-Time Markov Chain\nProcess, which occurs as a result of observing whether the time between states in a\nrandom walk is discrete or continuous. Each of its components is exemplified, and\nanalytically all the examples are solved.</jats:p>","journal":"Markov Chain Process (Theory and Cases)","year":2023,"id":29412,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":162264,"name":"Carlos Polanco","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.0,"endowment":0.0,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W4379794419","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.15283198,"influential_citations":0,"citation_trend":[],"oa_status":"closed","license":null,"oa_locations":[{"url":"http://dx.doi.org/10.2174/9789815080476123010009","host_type":"ebook platform"}],"fields_of_study":["Software System Performance and Reliability"],"mesh_terms":[],"keywords":["Markov chain","Markov property","Markov renewal process","Continuous-time Markov chain","Balance equation","Markov process","Variable-order Markov model","Markov chain mixing time","Additive Markov chain","Examples of Markov chains","Markov model","Discrete phase-type distribution","Markov kernel","Mathematics","Time reversibility","Absorbing Markov chain","Computer science","Stochastic matrix","Discrete time and continuous time","Statistics"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Reduced inequalities"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-08T23:42:47.893222Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}