(The) first return time and entropy of Markov chains = 마르코프 연쇄의 최초회귀시간과 엔트로피

The convergence rate of the expectation of the logarithm of the first return time is investigated. An algorithm for obtaining the probability distribution of the first return time for the initial n-block with overlapping is presented. For a Markov chain it is shown that $R_n(x)P_n(x)$ converges to exponential distribution in distribution and that $E[log(R_n(x)P_n(x))]$ converges to Euler`s constant, where $R_n(x)$ is the first return time of the initial n-block $x_1…x_n$ and $P_n(x)$ is the probability of $x_1…x_n$. The nonoverlapping first return time $R_(n)$ for ψ-mixing processes holds the same formula. A formula is proposed for measuring entropy for the given Markov chain and some simulation is done to show the accuracy of it. Finally, the algorithm for the probability distribution is applied to test the performance of pseudorandom number generators.
Advisors
Choe, Geon-Horesearcher최건호researcher
Publisher
한국과학기술원
Issue Date
2002
Identifier
174558/325007 / 000965054
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2002.2, [ [iii], 98 p. ]

Keywords

마르코프 연쇄; first return time; entropy; Markov chian; 최초회귀시간; 엔트로피

URI
http://hdl.handle.net/10203/41846
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=174558&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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