Statistical Identification of Markov Chain on Trees
| Autor: | Xuyan Xiang, Xiaoyun Mo, Xiao Zhang |
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| Rok vydání: | 2018 |
| Předmět: |
Correctness
Article Subject Markov chain Computer science lcsh:Mathematics General Mathematics General Engineering Hitting time Univariate Observable lcsh:QA1-939 Transition rate matrix 01 natural sciences 010104 statistics & probability lcsh:TA1-2040 0103 physical sciences 0101 mathematics lcsh:Engineering (General). Civil engineering (General) 010306 general physics Algorithm |
| Zdroj: | Mathematical Problems in Engineering, Vol 2018 (2018) |
| ISSN: | 1563-5147 1024-123X |
| DOI: | 10.1155/2018/2036248 |
| Popis: | The theoretical study of continuous-time homogeneous Markov chains is usually based on a natural assumption of a known transition rate matrix (TRM). However, the TRM of a Markov chain in realistic systems might be unknown and might even need to be identified by partially observable data. Thus, an issue on how to identify the TRM of the underlying Markov chain by partially observable information is derived from the great significance in applications. That is what we call the statistical identification of Markov chain. The Markov chain inversion approach has been derived for basic Markov chains by partial observation at few states. In the current letter, a more extensive class of Markov chain on trees is investigated. Firstly, a type of a more operable derivative constraint is developed. Then, it is shown that all Markov chains on trees can be identified only by such derivative constraints of univariate distributions of sojourn time and/or hitting time at a few states. A numerical example is included to demonstrate the correctness of the proposed algorithms. |
| Databáze: | OpenAIRE |
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