Mike Carter, C. C. Price, G. Rabadi
{"title":"Markov processes","authors":"Mike Carter, C. C. Price, G. Rabadi","doi":"10.1142/9789813273443_0003","DOIUrl":"https://doi.org/10.1142/9789813273443_0003","url":null,"abstract":"1 General Properties of Markov Processes 2 1.1 Discrete Time Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Continuous Time Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Waiting Times and Discrete Time Embedding . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Spectral Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Detailed Balance and Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.1 Self-Adjoint Symmetry and Spectral Decomposition . . . . . . . . . . . . . . . . . . . 11 1.4.2 Steady State Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4.3 Detailed Balance in Physical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 Entropy and the Approach to Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 The Backward Equation and Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.7 Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.8 The Deterministic Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19","PeriodicalId":433557,"journal":{"name":"Fractional Dynamics in Comb-like Structures","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124279759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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