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3 - Convolution Semigroups of Measures

Published online by Cambridge University Press:  27 July 2019

David Applebaum
Affiliation:
University of Sheffield
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Summary

Chapter 3 studies semigroups on function spaces obtained via convolution semigroups of probability measures. Motivating examples that are studied in detail are the heat kernel (Brownian motion) and the Poisson kernel (Cauchy process). The characteristic functional (Fourier transform) is used to establish the Levy–Khinchine formula, and applications are given to stable laws. The generator and the semigroup are written as pseudo-differential operators.

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Chapter
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Semigroups of Linear Operators
With Applications to Analysis, Probability and Physics
, pp. 46 - 82
Publisher: Cambridge University Press
Print publication year: 2019

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