• The Mathematical Education
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• v.25 no.1
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• pp.1-8
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• 1986

It is a common saying that markov-chain is a special case of probability course. That is to say, It means an unchangeable markov-chain process of the transition-probability of discontinuous time. There are two kinds of ways to show transition probability parade matrix theory. The first is the way by arrangement of a rightangled tetragon. The second part is a vertical measurement and direction sing by transition-circle. In this essay, I try to find out existence of procession for transition-probability applied markov-chain. And it is possible for me to know not only, what it is basic on a study of chain but also being applied to abnormal problems following a flow change and statistic facts expecting to use as a model of air expansion in physics.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.541-553
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• 2012

In this paper, we study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain on the generalized gambling system indexed by a tree by constructing a nonnegative martingale. As corollary, we obtain the property of the harmonic mean and the arithmetic mean of random transition probability for a second-order nonhomogeneous Markov chain indexed by a double root tree.

• Journal of Wind Energy
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• v.14 no.1
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• pp.37-43
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• 2023

In this study, synthetic time series wind data was generated numerically using a second-order Markov chain. One year of wind data in 2020 measured by the AWS on Wido Island was used to investigate the statistics for measured wind data. Both the transition probability matrix and the cumulative transition probability matrix for annual hourly mean wind speed were obtained through statistical analysis. Probability density distribution along the wind speed and autocorrelation according to time were compared with the first- and the second-order Markov chains with various lengths of time series wind data. Probability density distributions for measured wind data and synthetic wind data using the first- and the second-order Markov chains were also compared to each other. For the case of the second-order Markov chain, some improvement of the autocorrelation was verified. It turns out that the autocorrelation converges to zero according to increasing the wind speed when the data size is sufficiently large. The generation of artificial wind data is expected to be useful as input data for virtual digital twin wind turbines.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.8 no.3
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• pp.1-10
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• 2009

Bus delay time is occurred as the result of traffic condition and important factor to predict bus arrival time. In this paper, transition probability matrixes between bus stops are made by using Markov Chain and it is predicted bus delay time with them. As the results of study, it is confirmed a possibility of adapting the assumption which it has same bus transition probability between stops through paired-samples T-test and overcame the limitation of exiting studies in case there is no scheduled bus arrival time for each stops with using bus interval time. Therefore it will be possible to predict bus arrival time with Markov Chain.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.983-992
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• 1996

Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.537-564
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• 2023

In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ℤ^d, whose one-step transition probability is comparable to |x - y|^-dϕ_j (|x - y|)^-1 with ϕ_j being a positive regularly varying function on [1, ∞) with index α ∈ [2, ∞). For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

• Journal of the Korea Institute of Military Science and Technology
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• v.2 no.2
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• pp.131-139
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• 1999

An easy and efficient method is proposed for a computation of reliability of preprocessing filters in the fire control system when the sensor data are frequently unreliable depending on the operation environment. It computes state transition probability matrix after modeling filter states as a Markov process, and computing false alarm and detection probability of each filter state under the given sensor failure probability. It shows that two important indices such as distributed state probability and error variance can be derived easily for a reliability assessment of the given sensor fusion system.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.5
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• pp.1010-1019
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• 2004

In this paper, we represent Nakagami-m fading channel as finite-State Markov Channel (FSMC) and analyze the performance of wireless communication system with varying the fading channel condition. In FSMC model, the received signal's SNR is divided into finite intervals and these intervals are formed into Markov chain states. Each state is modeled by a BSC and the transition probability is dependent upon the physical characterization of the channel. The steady state probability and average symbol error rate of each state and transition probability are derived by numerical analysis and FSMC model is formed with these values. We found that various fading channels can be represented with FSMC by changing state transition index. In fast fading environment in which state transition index is large, the channel can be viewed as i.i.d. channel and on the contrary, in slow fading channel where state transition index is small, the channel can be represented by simple FSMC model in which transitions occur between just adjacent states. And we applied the proposed FSMC model to analyze the coding gain of random error correcting code on various fading channels via computer simulation.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.135-145
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• 2014

The present study surveys Bayesian modeling structure for inferences about transition probabilities of Markov chain. The motivation of the study came from the data that shows transitional behaviors of emotionally disturbed children undergoing residential treatment program. Dirichlet distribution was used as prior for the multinomial distribution. The analysis with real data was implemented in WinBUGS programming environment. The performance of the model was compared to that of alternative approaches.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.1-9
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• 2007

A three-state Markov logistic regression model is suggested to forecast the probability of tomorrow's precipitation based on the current meteorological situation. The suggested model turns out to be better than Markov regression model in the sense of the mean squared error of forecasting for the rainfall data of Seoul area.