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Markovian Dynamics

In: Discrete Stochastics

Author

Listed:
  • Konrad Jacobs

    (Universität Erlangen-Nürnberg, Mathematisches Institut)

Abstract

In many cases the evolution of certain phenomena can be interpreted as changes of the state of a dynamical system. A finite-state dynamical system consists of a finite “state space” D and a mapping T : D → D. The interpretation is: if the system is in state j ∈ D at time t, it will be in state k = T(j) at time t + 1. Such finite state discrete-time dynamical systems are much too primitive to describe important phenomena like the evolution of the plantetary system or the like; continuous state spaces and continuous time are a characteristic of most full-fledged dynamical systems, and calculus is the proper tool for their investigation; actually, calculus was invented for this purpose.

Suggested Citation

  • Konrad Jacobs, 1992. "Markovian Dynamics," Springer Books, in: Discrete Stochastics, chapter 0, pages 19-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8645-1_2
    DOI: 10.1007/978-3-0348-8645-1_2
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