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.
KeywordsBoltzmann, L. Brownian motion Ergodic theory Gibbs, G. Markov processes Markov property Newton’s equation Probability Statistical mechanics Wiener process
- Karlin, S., and H. Taylor. 1975. A first course in stochastic processes. 2nd ed. New York: Academic Press.Google Scholar
- Norris, J. 1997. Markov chains. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.Google Scholar
- Stroock, D. 2005. An introduction to Markov processes. Graduate Text Series No. 230. Heidelberg: Springer-Verlag.Google Scholar
- Dynkin, E. 1965. Markov processes, vols. 1 and 2. Grundlehren Nos. 121 and 122. Heidelberg: Springer-Verlag.Google Scholar
- Revuz, D. 1984. Markov chains. North-Holland Mathematical Library, vol. 11. Amsterdam and New York: North-Holland.Google Scholar
- Stroock, D. 2003. Markov processes from K. Itô’s perspective. Annals of Mathematical Studies No. 155. Princeton: Princeton University Press.Google Scholar