Elements of the Theory of Markov Processes and Their ApplicationsThis graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition. |
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Page 13
... asymptotic behavior of the pg'), which in turn enables us to study the asymptotic behavior of the absolute probabilities. D. Classification of States. Given a Markov chain {X,,, n = 0, 1, . . .}, its states can be classified in a number ...
... asymptotic behavior of the pg'), which in turn enables us to study the asymptotic behavior of the absolute probabilities. D. Classification of States. Given a Markov chain {X,,, n = 0, 1, . . .}, its states can be classified in a number ...
Page 15
... asymptotic behavior of pg'), we state and prove a fundamental theorem which establishes a relationship between the pi? and Q”. Theorem 1.1: Consider the series °° ( 211%?) (117) ,,= If (1.17) converges, then Q” = 0. (This is always true ...
... asymptotic behavior of pg'), we state and prove a fundamental theorem which establishes a relationship between the pi? and Q”. Theorem 1.1: Consider the series °° ( 211%?) (117) ,,= If (1.17) converges, then Q” = 0. (This is always true ...
Page 27
... asymptotic behavior of sequences of random variables associated with stochastic models in various applications. In this section we shall study some limit theorems which are concemed with the following: 1. The n-step transition ...
... asymptotic behavior of sequences of random variables associated with stochastic models in various applications. In this section we shall study some limit theorems which are concemed with the following: 1. The n-step transition ...
Page 37
... asymptotic theory associated with X,,. However, Yaglom [63] has shown that, if we consider the conditional distribution of X", given that X,, ¢ 0, then we obtain nontrivial limiting distributions. Yaglom's results are given by Theorems ...
... asymptotic theory associated with X,,. However, Yaglom [63] has shown that, if we consider the conditional distribution of X", given that X,, ¢ 0, then we obtain nontrivial limiting distributions. Yaglom's results are given by Theorems ...
Page 43
... asymptotic expressions for the probabilities q(z)~ 1.7 Representation as Random-walk Processes A. Introduction. In many applied problems the generatingfunction representation of a discrete branching process leads to mathematical ...
... asymptotic expressions for the probabilities q(z)~ 1.7 Representation as Random-walk Processes A. Introduction. In many applied problems the generatingfunction representation of a discrete branching process leads to mathematical ...
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Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |
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