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.
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Bibliography
Elementary Texts
Karlin, S., and H. Taylor. 1975. A first course in stochastic processes. 2nd ed. New York: Academic Press.
Norris, J. 1997. Markov chains. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.
Stroock, D. 2005. An introduction to Markov processes. Graduate Text Series No. 230. Heidelberg: Springer-Verlag.
Advanced Texts
Dynkin, E. 1965. Markov processes, vols. 1 and 2. Grundlehren Nos. 121 and 122. Heidelberg: Springer-Verlag.
Ethier, S., and T. Kurtz. 1986. Markov processes: Characterization and convergence. New York: Wiley.
Revuz, D. 1984. Markov chains. North-Holland Mathematical Library, vol. 11. Amsterdam and New York: North-Holland.
Stroock, D. 2003. Markov processes from K. Itô’s perspective. Annals of Mathematical Studies No. 155. Princeton: Princeton University Press.
Physics Texts
Boltzmann, L. 1896, 1898. Lectures on gas theory,vols. 2, Trans. S. Brush. New York: Dover Publications, 1995.
Gibbs, J. 1902. Elementary principles in statistical mechanics. New York: Scribner.
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Stroock, D.W. (2018). Markov Processes. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2668
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2668
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Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
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