Elements of the Theory of Markov Processes and Their ApplicationsGraduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition. |
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Page 29
... Hence , for every N < > 0 we can select an N such that Σ K N terms in the series p - N n n = 1 ΣKp y = 1 = 1 e . Now , the last ― differ arbitrarily little from 7 , K , and hence from 7. Finally , the sum of the first n = 1 ∞ n - N ...
... Hence , for every N < > 0 we can select an N such that Σ K N terms in the series p - N n n = 1 ΣKp y = 1 = 1 e . Now , the last ― differ arbitrarily little from 7 , K , and hence from 7. Finally , the sum of the first n = 1 ∞ n - N ...
Page 84
Albert T. Bharucha-Reid. Similar calculations for the second moment give hence ( 1 + x ) m2 ( t ) + m ( t ) = ( 1 + a ) ( 2t ) 2 + 2t D2 { X ( t ) } = λι ( 1 + αλέ ) ( 2.128 ) Hence , for the Pólya process the mean is a linear function ...
Albert T. Bharucha-Reid. Similar calculations for the second moment give hence ( 1 + x ) m2 ( t ) + m ( t ) = ( 1 + a ) ( 2t ) 2 + 2t D2 { X ( t ) } = λι ( 1 + αλέ ) ( 2.128 ) Hence , for the Pólya process the mean is a linear function ...
Page 250
... Hence , we assume that the probability of having one particle in the interval dE is proportional to dE , and the probability of n ( n > 1 ) particles being in dE is 0 ( dE ) " . Let then & { nk } = Σ P2nk n = 0 & { n } = & { [ dX ( E ...
... Hence , we assume that the probability of having one particle in the interval dE is proportional to dE , and the probability of n ( n > 1 ) particles being in dE is 0 ( dE ) " . Let then & { nk } = Σ P2nk n = 0 & { n } = & { [ dX ( E ...
Other editions - View all
Elements of the Theory of Markov Processes and Their Applications A. T. Bharucha-Reid Limited preview - 2012 |
Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |
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