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Markov Processes


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Random Variable Theory General Features of a Markov Process Continuous Markov Processes Jump Markov Processes with Continuum States Jump Markov Processes with Discrete States Temporally Homogeneous Birth-Death Markov Processes Appendixes: Some Useful Integral Identities Integral Representations of the Delta Functions An Approximate Solution Procedure for "Open" Moment Evolution Equations Estimating the Width and Area of a Function Peak Can the Accuracy of the Continuous Process Simulation Formula Be Improved? Proof of the Birth-Death Stability Theorem Solution of the Matrix Differential Equation

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Key Features * A self-contained, prgamatic exposition of the needed elements of random variable theory * Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations * Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples * Clear treatments of first passages, first exits, and stable state fluctuations and transitions * Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

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