Ergodic Theory and Diffusion Theory

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

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

Manifold Convolution Hunt Dition 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1968

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Department of MathematicsUniversity of TokyoTokyoJapan

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