Abstract
We have seen several examples on how to calculate a characteristic function when given a random variable. Equivalently we have seen examples of how to calculate the Fourier transforms of probability measures. For such transforms to be useful, we need to know that knowledge of the transform characterizes the distribution that gives rise to it. The proof of the next theorem uses the Stone-Weierstrass theorem and thus is a bit advanced for this book. Nevertheless we include the proof for the sake of completeness.
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© 2000 Springer-Verlag Berlin Heidelberg
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Jacod, J., Protter, P. (2000). Properties of Characteristic Functions. In: Probability Essentials. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51431-9_14
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DOI: https://doi.org/10.1007/978-3-642-51431-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66419-2
Online ISBN: 978-3-642-51431-9
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