Abstract
In Chapter 17 we studied convergence theorems, but they were all of the type that one form of convergence, plus perhaps an extra condition, implies another type of convergence. What is unusual about martingale convergence theorems is that no type of convergence is assumed — only a certain structure — yet convergence is concluded. This makes martingale convergence theorems special in analysis; the only similar situation arises in ergodic theory.
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© 2000 Springer-Verlag Berlin Heidelberg
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Jacod, J., Protter, P. (2000). Martingale Convergence Theorems. In: Probability Essentials. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51431-9_27
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DOI: https://doi.org/10.1007/978-3-642-51431-9_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66419-2
Online ISBN: 978-3-642-51431-9
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