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 2
... differential equation £62 _ dt _ Z:c(t) (0.1) If we assume that x(0) = x0 > 0, then the solution of Eq. (0.1) is x(t) = woe“ (0-2) In this simple model we have not made any assumption about the removal of bacteria from the population ...
... differential equation £62 _ dt _ Z:c(t) (0.1) If we assume that x(0) = x0 > 0, then the solution of Eq. (0.1) is x(t) = woe“ (0-2) In this simple model we have not made any assumption about the removal of bacteria from the population ...
Page 61
A. T. Bharucha-Reid. equation, since it involves differentiation with respect to the ... differential equations were first derived by Kolmogorov [56] in a ... equation is now written as P.-no =§oP..<¢,8)P.,(8.t> <2-25> for all t > 1 ...
A. T. Bharucha-Reid. equation, since it involves differentiation with respect to the ... differential equations were first derived by Kolmogorov [56] in a ... equation is now written as P.-no =§oP..<¢,8)P.,(8.t> <2-25> for all t > 1 ...
Page 64
... differential equation %@= dt az(t) has the solution z(t) : z(())e'". This suggests that the solution of (2.40) can ... Differential Equations. In this section we consider the existence and uniqueness theory for the Kolmogorov equations ...
... differential equation %@= dt az(t) has the solution z(t) : z(())e'". This suggests that the solution of (2.40) can ... Differential Equations. In this section we consider the existence and uniqueness theory for the Kolmogorov equations ...
Page 72
... equations with P,»,(t) > 0, and}: P,,(t) < 1. In addition, P,~0j(t0) ¢ F,-0,-(to) for any j with -=1 C, >7 0, so that P(t) is different from F(t). In ... differential-difference equation describing the probability 72 THEORY OF.MARKOV PROGE%M$
... equations with P,»,(t) > 0, and}: P,,(t) < 1. In addition, P,~0j(t0) ¢ F,-0,-(to) for any j with -=1 C, >7 0, so that P(t) is different from F(t). In ... differential-difference equation describing the probability 72 THEORY OF.MARKOV PROGE%M$
Page 73
... differential-difl'erence equation,1 our main purpose being to illustrate the various methods that are available for treating stochastic differential-difference equations. B. The Poisson Process. The Poisson process is the simplest of ...
... differential-difl'erence equation,1 our main purpose being to illustrate the various methods that are available for treating stochastic differential-difference equations. B. The Poisson Process. The Poisson process is the simplest of ...
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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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