A modification of a result due to Moran

1968 ◽  
Vol 5 (01) ◽  
pp. 220-223 ◽  
Author(s):  
Barry C. Arnold
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Transition Probability ◽  
Transition Probability Matrix

Let {X(n): n = 0, 1, 2, …} be a Markov chain with state space {0, 1, 2, …, N} and transition probability matrix P = (pij ).

Some explicit results for correlated random walks

1989 ◽  
Vol 26 (4) ◽  
pp. 757-766 ◽  
Author(s):  
Ram Lal ◽  
U. Narayan Bhat
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Equilibrium Distribution ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Correlated Random Walks ◽  
Finite State ◽  
Direction Of Movement ◽  
Step Transition

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

Some explicit results for correlated random walks

1989 ◽  
Vol 26 (04) ◽  
pp. 757-766 ◽  
Author(s):  
Ram Lal ◽  
U. Narayan Bhat
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Equilibrium Distribution ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Correlated Random Walks ◽  
Finite State ◽  
Direction Of Movement ◽  
Step Transition

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

Weak lumpability in finite Markov chains

1982 ◽  
Vol 19 (03) ◽  
pp. 685-691 ◽  
Author(s):  
Atef M. Abdel-moneim ◽  
Frederick W. Leysieffer
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Transition Probability ◽  
Linear Equations ◽  
Transition Probability Matrix ◽  
Finite Markov Chain ◽  
Systems Of Linear Equations ◽  
Finite Markov Chains ◽  
The Given

Criteria are given to determine whether a given finite Markov chain can be lumped weakly with respect to a given partition of its state space. These conditions are given in terms of solution classes of systems of linear equations associated with the transition probability matrix of the Markov chain and the given partition.

Weak lumpability in finite Markov chains

1982 ◽  
Vol 19 (3) ◽  
pp. 685-691 ◽  
Author(s):  
Atef M. Abdel-moneim ◽  
Frederick W. Leysieffer
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Transition Probability ◽  
Linear Equations ◽  
Transition Probability Matrix ◽  
Finite Markov Chain ◽  
Systems Of Linear Equations ◽  
Finite Markov Chains ◽  
The Given

Criteria are given to determine whether a given finite Markov chain can be lumped weakly with respect to a given partition of its state space. These conditions are given in terms of solution classes of systems of linear equations associated with the transition probability matrix of the Markov chain and the given partition.

A modification of a result due to Moran

1968 ◽  
Vol 5 (1) ◽  
pp. 220-223 ◽  
Author(s):  
Barry C. Arnold
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Transition Probability ◽  
Transition Probability Matrix

Let {X(n): n = 0, 1, 2, …} be a Markov chain with state space {0, 1, 2, …, N} and transition probability matrix P = (pij).

The censored Markov chain and the best augmentation

1996 ◽  
Vol 33 (03) ◽  
pp. 623-629 ◽  
Author(s):  
Y. Quennel Zhao ◽  
Danielle Liu
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
The Best Approximation ◽  
Finite Matrix ◽  
Countable State ◽  
Stationary Probabilities

Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite matrix. Different augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this paper, we prove that the censored (watched) Markov chain provides the best approximation in the sense that, for a given truncation size, the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

2018 ◽  
Vol 28 (5) ◽  
pp. 1552-1563 ◽  
Author(s):  
Tunny Sebastian ◽  
Visalakshi Jeyaseelan ◽  
Lakshmanan Jeyaseelan ◽  
Shalini Anandan ◽  
Sebastian George ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Markov Chain ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Passage Time ◽  
Transition Probability Matrix ◽  
Ordinal Logistic Regression ◽  
The Mean

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as ‘Low’, ‘Moderate’ and ‘High’ with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

scholarly journals Frekuensi Hari Hujan Menurut Bulan di Kota Balikpapan dengan Rantai Markov Waktu Diskrit

2019 ◽  
Vol 1 (2) ◽  
pp. 5-10
Author(s):  
Muhammad Azka
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Transition Diagram ◽  
Discrete Time Markov Chain ◽  
Applied Method ◽  
Frequency Rate

The problem proposed in this research is about the amount rainy day per a month at Balikpapan city and discretetime markov chain. The purpose is finding the probability of rainy day with the frequency rate of rainy at the next month if given the frequency rate of rainy at the prior month. The applied method in this research is classifying the amount of rainy day be three frequency levels, those are, high, medium, and low. If a month, the amount of rainy day is less than 11 then the frequency rate for the month is classified low, if a month, the amount of rainy day between 10 and 20, then it is classified medium and if it is more than 20, then it is classified high. The result is discrete-time markov chain represented with the transition probability matrix, and the transition diagram.

scholarly journals Complex Probability and Markov Stochastic Process

2019 ◽  
Vol 3 (1) ◽  
pp. 13-22
Author(s):  
Bijan Bidabad ◽  
Behrouz Bidabad
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Real World ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
The Real ◽  
Definition Of ◽  
Discrete Markov Chain

This note discusses the existence of "complex probability" in the real world sensible problems. By defining a measure more general than the conventional definition of probability, the transition probability matrix of discrete Markov chain is broken to the periods shorter than a complete step of the transition. In this regard, the complex probability is implied.

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