{"title":"两态马尔可夫链高差结构的完全随机性","authors":"A. Shahverdian","doi":"10.1109/csitechnol.2017.8312134","DOIUrl":null,"url":null,"abstract":"The paper studies the higher-order absolute differences taken from progressive terms of time-homogeneous binary Markov chains. Two theorems presented are the limiting theorems for these differences, when their order k converges to infinity. Theorems 1 and 2 assert that there exist some infinite subsets E of natural series such that kth order differences of every such chain converge to the equi-distributed random binary process as k growth to infinity remaining on E. The chains are classified into two types, and E depends only on the type of the given chain. Two kinds of discrete capacities for subsets of natural series are defined, and in their terms such sets E are described.","PeriodicalId":332371,"journal":{"name":"2017 Computer Science and Information Technologies (CSIT)","volume":"17 3","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Full randomness in the higher difference structure of two-state Markov chains\",\"authors\":\"A. Shahverdian\",\"doi\":\"10.1109/csitechnol.2017.8312134\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper studies the higher-order absolute differences taken from progressive terms of time-homogeneous binary Markov chains. Two theorems presented are the limiting theorems for these differences, when their order k converges to infinity. Theorems 1 and 2 assert that there exist some infinite subsets E of natural series such that kth order differences of every such chain converge to the equi-distributed random binary process as k growth to infinity remaining on E. The chains are classified into two types, and E depends only on the type of the given chain. Two kinds of discrete capacities for subsets of natural series are defined, and in their terms such sets E are described.\",\"PeriodicalId\":332371,\"journal\":{\"name\":\"2017 Computer Science and Information Technologies (CSIT)\",\"volume\":\"17 3\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 Computer Science and Information Technologies (CSIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/csitechnol.2017.8312134\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 Computer Science and Information Technologies (CSIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/csitechnol.2017.8312134","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Full randomness in the higher difference structure of two-state Markov chains
The paper studies the higher-order absolute differences taken from progressive terms of time-homogeneous binary Markov chains. Two theorems presented are the limiting theorems for these differences, when their order k converges to infinity. Theorems 1 and 2 assert that there exist some infinite subsets E of natural series such that kth order differences of every such chain converge to the equi-distributed random binary process as k growth to infinity remaining on E. The chains are classified into two types, and E depends only on the type of the given chain. Two kinds of discrete capacities for subsets of natural series are defined, and in their terms such sets E are described.