Israel Journal of Mathematics

, Volume 4, Issue 1, pp 11–22 | Cite as

The ergodic theorem for Markov processes

  • S. R. Foguel


Most of the material in Sections 4-5-6-8-11 has been published in [4]-[10]. We shall deal with the asymptotical behavior of the iterates of a Markov transition function. Our aim is to generalize the results about the ‘cyclic’ convergence of the iterates of a Markov matrix. Throughout the paper functional analytic methods are used and not probabilistic arguments. The report is self contained, modulo standart results from functional analysis, except for the decomposition into conservative and dissipative parts. Also we assume the existence of an invariant σ finite measure on the conservative part. This has been proved, under some restrictions, by several authors using probabilistic methods.


Hilbert Space Markov Process Invariant Measure Ergodic Theorem Finite Measure 
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Copyright information

© Hebrew University 1966

Authors and Affiliations

  • S. R. Foguel
    • 1
  1. 1.The Hebrew University of JerusalemIsrael

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