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Continuous Time Processes

  • Frank A. Haight
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 23)

Abstract

There is a fundamental difference between the mathematical formulation of a discrete time stochastic process and a continuous time stochastic process. In discrete time, it is necessary to specify only the mechanism for transition from one state to another, and of course the initial state (distribution) of the system. For Markov chains, this consists of the transition matrix and the initial vector. Everything about the chain can, in principle, be deduced from this matrix and vector.

Keywords

Point Process Renewal Process Sojourn Time Probability Generate Function Counting Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. Çinlar, Erhan (1975), Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  2. Cox, D. R. (1962), Renewal Theory, John Wiley and Sons, New York.Google Scholar
  3. Cox, D. R., and Miller, H. D. (1965), The Theory of Stochastic Processes, Methuen, London.Google Scholar
  4. Hoel, Paul G., Port, Sidney C., and Stone, Charles J. (1972), Introduction to Stochastic Processes, Houghton Mifflin, Boston.Google Scholar
  5. Karlin, Samuel, and Taylor, Howard M., (1975), A First Course in Stochastic Processes, Academic Press, New York.Google Scholar
  6. Ross, Sheldon M. (1972), Introduction to Probability Models, Academic Press, New York.Google Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Frank A. Haight
    • 1
  1. 1.The Pennsylvania State UniversityPennsylvaniaUSA

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