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 9
... number of states, as well as some special limit theorems for branching processes. In Sec. 1.7 we consider a simple random-walk process on the nonnegative integers and discuss the relationship between randomwalk processes 9.
... number of states, as well as some special limit theorems for branching processes. In Sec. 1.7 we consider a simple random-walk process on the nonnegative integers and discuss the relationship between randomwalk processes 9.
Page 10
... nonnegative integers x = 0, 1, 2, . . . . Hence the processes we consider in this chapter are discrete with respect to both the state variable as and the time variable n. The process {X,,, n = 0, 1, 2, . . will be said to represent a ...
... nonnegative integers x = 0, 1, 2, . . . . Hence the processes we consider in this chapter are discrete with respect to both the state variable as and the time variable n. The process {X,,, n = 0, 1, 2, . . will be said to represent a ...
Page 11
... nonnegative integers, we can be more precise and say that the discrete branching process is a special case of a Markov chain with a denumerable-number of states. This class of Markov chains was first considered by Kolmogorov [43]1 in ...
... nonnegative integers, we can be more precise and say that the discrete branching process is a special case of a Markov chain with a denumerable-number of states. This class of Markov chains was first considered by Kolmogorov [43]1 in ...
Page 12
... nonnegative elements, since p,-, 2 0 for all i and j, and with row sums equal to unity, since 210” = 1 '=0 for all i. A matrix satisfying the above conditions is called ajstochastic, or Markov, matrix.1 A Markov chain is completely ...
... nonnegative elements, since p,-, 2 0 for all i and j, and with row sums equal to unity, since 210” = 1 '=0 for all i. A matrix satisfying the above conditions is called ajstochastic, or Markov, matrix.1 A Markov chain is completely ...
Page 25
... nonnegative. In addition, F(0) : p(0) > 0 and F(1) = 1; hence, F(s) is monotone increasing in the interval [0,1]. Now let to be the first nonnegative fixed point of F(s). ___ 1 4 | I I 1 1 | 1 1 I 1 I 1 ( I I I I 1. O.
... nonnegative. In addition, F(0) : p(0) > 0 and F(1) = 1; hence, F(s) is monotone increasing in the interval [0,1]. Now let to be the first nonnegative fixed point of F(s). ___ 1 4 | I I 1 1 | 1 1 I 1 I 1 ( I I I I 1. O.
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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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