Ergodic Theory and Diffusion Theory

  • Kôsaku Yosida
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)


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 semigroup T i , 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.


Markov Process Invariant Measure Ergodic Theory Bounded Linear Operator Ergodic Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Research Institute for Mathematical SciencesUniversity of KyotoKyotoJapan

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