A Non-Stationary Transition Probabilities for a Reservoir elevation of Hydro Electric Power Dam

2014 ◽  
Vol 10 (3) ◽  
pp. 39-44
Author(s):  
Abubakar U.Y ◽  
◽  
Hakimi D ◽  
Mohammed A ◽  
Lawal A
Keyword(s):  
Electric Power ◽  
Transition Probabilities ◽  
Stationary Transition

Markov Chains with Stationary Transition Probabilities

1961 ◽  
Vol 45 (354) ◽  
pp. 362
Author(s):  
D. G. Kendall ◽  
Kai Lai Chung
Keyword(s):  
Markov Chains ◽  
Transition Probabilities ◽  
Stationary Transition

Multivariate extremal processes, leader processes and dynamic choice models

1990 ◽  
Vol 22 (2) ◽  
pp. 309-331 ◽  
Author(s):  
Sidney Resnick ◽  
Rishin Roy
Keyword(s):  
Transition Probabilities ◽  
Homogeneous Case ◽  
Dynamic Choice ◽  
Underlying Distribution ◽  
Extremal Process ◽  
Time Dependent Behaviour ◽  
Stationary Transition ◽  
Dynamic Choice Models ◽  
Dependent Behaviour ◽  
Leader Process

Let (Y(t), t > 0) be a d-dimensional non-homogeneous multivariate extremal process. We suppose the ith component of Y describes time-dependent behaviour of random utilities associated with the ith choice. At time t we choose the ith alternative if the ith component of Y(t) is the largest of all the components. Let J(t) be the index of the largest component at time t so J has range {1, …, d} and call {J(t)} the leader process. Let Z(t) be the value of the largest component at time t. Then the bivariate process (J(t), Z(t)} is Markov. We discuss when J(t) and Z(t) are independent, when {J(s), 0<s≦t} and Z(t) are independent and when J(t) and {Z(s), 0<s≦t} are independent. In usual circumstances, {J(t)} is Markov and particular properties are given when the underlying distribution is max-stable. In the max-stable time-homogeneous case, {J(et)} is a stationary Markov chain with stationary transition probabilities.

Modeling the effect of erosion on crop production

1987 ◽  
Vol 24 (4) ◽  
pp. 787-797 ◽  
Author(s):  
P. Todorovic ◽  
J. Gani
Keyword(s):  
Crop Yield ◽  
Crop Production ◽  
Transition Probabilities ◽  
Past History ◽  
Random Variable ◽  
Linear Integral Equation ◽  
Regularity Conditions ◽  
Almost Everywhere ◽  
Stationary Transition ◽  
Linear Integral

This paper is concerned with a model for the effect of erosion on crop production. Crop yield in the year n is given by X(n) = YnLn, where is a sequence of strictly positive i.i.d. random variables such that E{Y1} <∞, and is a Markov chain with stationary transition probabilities, independent of . When suitably normalized, leads to a martingale which converges to 0 almost everywhere (a.e.) as n → ∞. In addition, for large n, the distribution of Ln is approximately lognormal. The conditional expectations and probabilities of , given the past history of the process, are determined. Finally, the asymptotic behaviour of the total crop yield is discussed. It is established that under certain regularity conditions Sn converges a.e. to a finite-valued random variable S whose Laplace transform can be obtained as the solution of a Volterra-type linear integral equation.

Limit theorems for sums of a sequence of random variables defined on a Markov chain

1977 ◽  
Vol 14 (03) ◽  
pp. 614-620
Author(s):  
David B. Wolfson
Keyword(s):  
Limit Theorems ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Renewal Theory ◽  
Strong Mixing ◽  
Mixing Condition ◽  
The Matrix ◽  
Stationary Transition ◽  
Positive Recurrent ◽  
Markov Renewal Theory

Let {(Jn, Xn),n≧ 0} be the standardJ–Xprocess of Markov renewal theory. Suppose {Jn,n≧ 0} is irreducible, aperiodic and positive recurrent. It is shown using the strong mixing condition, that ifconverges in distribution, wherean, bn&gt;0 (bn→∞) are real constants, then the limit lawFmust be stable. SupposeQ(x) = {PijHi(x)} is the semi-Markov matrix of {(JnXn),n≧ 0}. Then then-fold convolution,Q∗n(bnx + anbn), converges in distribution toF(x)Π if and only ifconverges in distribution toF. Π is the matrix of stationary transition probabilities of {Jn,n≧ 0}. Sufficient conditions on theHi's are given for the convergence of the sequence of semi-Markov matrices toF(x)Π, whereFis stable.

Approximating kth-order two-state Markov chains

1992 ◽  
Vol 29 (4) ◽  
pp. 861-868 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Markov Chains ◽  
Total Variation ◽  
Upper Bound ◽  
Transition Probabilities ◽  
Random Variable ◽  
Poisson Random Variable ◽  
Compound Poisson ◽  
Stationary Transition

In this paper, we consider kth-order two-state Markov chains {Xi} with stationary transition probabilities. For k = 1, we construct in detail an upper bound for the total variation d(Sn, Y) = Σx |𝐏(Sn = x) − 𝐏(Y = x)|, where Sn = X1 + · ··+ Xn and Y is a compound Poisson random variable. We also show that, under certain conditions, d(Sn, Y) converges to 0 as n tends to ∞. For k = 2, the corresponding results are given without derivation. For general k ≧ 3, a conjecture is proposed.

scholarly journals A Markov Chain Analysis of Structural Changes in the Texas High Plains Cotton Ginning Industry

1985 ◽  
Vol 17 (2) ◽  
pp. 11-20 ◽  
Author(s):  
Don E. Ethridge ◽  
Sujit K. Roy ◽  
David W. Myers
Keyword(s):  
Markov Chain ◽  
Structural Changes ◽  
Transition Probabilities ◽  
High Plains ◽  
Markov Chain Analysis ◽  
West Texas ◽  
Texas High Plains ◽  
Chain Analysis ◽  
Stationary Transition ◽  
Number Of Firms

AbstractMarkov chain analysis of changes in the number and size of cotton gin firms in West Texas was conducted assuming stationary and non-stationary transition probabilities. Projections of industry structure were made to 1999 with stationary probability assumptions and six sets of assumed conditions for labor and energy costs and technological change in the non-stationary transition model. Results indicate a continued decline in number of firms, but labor, energy, and technology conditions alter the configuration of the structural changes.

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