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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Bibliography
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© 1995 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1995). Ergodic Theory and Diffusion Theory. In: Functional Analysis. Classics in Mathematics, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61859-8_14
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DOI: https://doi.org/10.1007/978-3-642-61859-8_14
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