The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Markov Processes

  • Daniel W. Stroock
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2668

Abstract

In this article the theory of Markov processes is described as an evolution on the space of probability measures. Following a brief historical account of its origins in physics, a mathematical formulation of the theory is given. Emphasis has been placed on the ergodic properties of Markov processes, and their presence is checked in a simple example.

Keywords

Boltzmann, L. Brownian motion Ergodic theory Gibbs, G. Markov processes Markov property Newton’s equation Probability Statistical mechanics Wiener process 

JEL Classifications

C6 
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Bibliography

Elementary Texts

  1. Karlin, S., and H. Taylor. 1975. A first course in stochastic processes. 2nd ed. New York: Academic Press.Google Scholar
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Advanced Texts

  1. Dynkin, E. 1965. Markov processes, vols. 1 and 2. Grundlehren Nos. 121 and 122. Heidelberg: Springer-Verlag.Google Scholar
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  3. Revuz, D. 1984. Markov chains. North-Holland Mathematical Library, vol. 11. Amsterdam and New York: North-Holland.Google Scholar
  4. Stroock, D. 2003. Markov processes from K. Itôs perspective. Annals of Mathematical Studies No. 155. Princeton: Princeton University Press.Google Scholar

Physics Texts

  1. Boltzmann, L. 1896, 1898. Lectures on gas theory,vols. 2, Trans. S. Brush. New York: Dover Publications, 1995.Google Scholar
  2. Gibbs, J. 1902. Elementary principles in statistical mechanics. New York: Scribner.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Daniel W. Stroock
    • 1
  1. 1.