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Markov Processes

  • ID: 1767814
  • Book
  • 592 Pages
  • Elsevier Science and Technology
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Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.

- 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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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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Gillespie, Daniel T.
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