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Abstract

These theories constitute fascinating fields of application of the analytical theory of semi-groups. Mathematically speaking, the ergodic theory is concerned with the “time average” \(\mathop{{\lim }}\limits_{{t \uparrow \infty }} {t^{{ - 1}}}\int\limits_{0}^{t} {{T_{s}}ds}\) of a semi-group T t , and the diffusion theory is concerned with the investigation of a stochastic process in terms of the infinitesimal generator of the semi-group intrinsically associated with the stochastic process.

Keywords

Markov Process Invariant Measure Ergodic Theory Bounded Linear Operator Ergodic Theorem 
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-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Gakushuin UniversityTokyoJapan

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