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Markov Processes \(\star \)

  • Simon ŠircaEmail author
Chapter
Part of the Graduate Texts in Physics book series (GTP)

Abstract

Markov processes are introduced as memoryless stochastic processes and classified in four classes based on whether the time parameter is continuous or discrete and whether the sample space is continuous or discrete. Two of them are treated in more detail: discrete-time (“classical”) Markov chains and continuous-time, continuous-state Markov processes. Long-time behavior of the chains is discussed, establishing the conditions for the formation of equilibrium distributions. In the continuous case, the Markov propagator is defined along with a discussion of moment functions, characterizing functions, and time evolution of the moments. Two particular Markov processes, the Wiener and the Ornstein–Uhlenbeck process, are given special attention due to their relevance for the study of diffusion.

Keywords

Markov Process Equilibrium Distribution Wiener Process Moment Function Planck Equation 
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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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