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The Splendors and Miseries of MartingalesMy Encounters with Martingales

The Splendors and Miseries of Martingales: My Encounters with Martingales [The text below describes the mathematical activities of Klaus Krickeberg during the period when he was working on martingales, along with many other different mathematical subjects. This period extends from 1946 to 1964. His main results about martingales (semi-martingales always admitted) may be summarized as follows: a) processes with a directed index set (Moore-Smith sequences) b) The “Krickeberg-decomposition” of martingales c) The discovery that the covering theorem by the mathematician Giuseppe Vitali in classical analysis implied some form of almost everywhere convergence of martingales d) Based on this he studied systematically sufficient conditions for such convergence which are in some way related to this covering theorem; he called them “Vitali-conditions” e) A convergence theorem including both increasing and decreasing martingales (Børge Jessen problem) f) Stochastic convergence of martingales.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesMy Encounters with Martingales

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn

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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
215 –221
DOI
10.1007/978-3-031-05988-9_10
Publisher site
See Chapter on Publisher Site

Abstract

[The text below describes the mathematical activities of Klaus Krickeberg during the period when he was working on martingales, along with many other different mathematical subjects. This period extends from 1946 to 1964. His main results about martingales (semi-martingales always admitted) may be summarized as follows: a) processes with a directed index set (Moore-Smith sequences) b) The “Krickeberg-decomposition” of martingales c) The discovery that the covering theorem by the mathematician Giuseppe Vitali in classical analysis implied some form of almost everywhere convergence of martingales d) Based on this he studied systematically sufficient conditions for such convergence which are in some way related to this covering theorem; he called them “Vitali-conditions” e) A convergence theorem including both increasing and decreasing martingales (Børge Jessen problem) f) Stochastic convergence of martingales.]

Published: Oct 18, 2022

Keywords: Martingales; Vitali conditions

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