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 semigroup 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.
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References
Feller’s original paper was published in 1952: Feller, W. [2]
The proof of Theorem 2 given above is adapted from Feller, W. [3]
and [4].
who also delivered an inspiring address [5]. We also refer the readers to the forthcoming book by Itô, K. [1] (with H. P. McKean) Diffusion Processes and Their Sample Paths, Springer, to appear and E. B. Dynkin [3], and the references given in these books.
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© 1965 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1965). Ergodic Theory and Diffusion Theory. In: Functional Analysis. Die Grundlehren der Mathematischen Wissenschaften, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25762-3_14
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DOI: https://doi.org/10.1007/978-3-662-25762-3_14
Publisher Name: Springer, Berlin, Heidelberg
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