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The Splendors and Miseries of MartingalesEncounters with Martingales in Stochastic Control

The Splendors and Miseries of Martingales: Encounters with Martingales in Stochastic Control [The martingale approach to stochastic control is very natural and avoids some major mathematical difficulties that arise when Hamilton-Jacobi-Bellman partial differential equations are used to solve optimization problems. The brief history of stochastic control given here commences with the war effort in the US in the 1940s, proceeds through the 1950s and 1960s, and touches on more recent aspects. This history shows that the solution of problems in potential theory related to stochastic control and other stochastic filtering problems is an important mathematical manifestation of martingales.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesEncounters with Martingales in Stochastic Control

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
321 –334
DOI
10.1007/978-3-031-05988-9_14
Publisher site
See Chapter on Publisher Site

Abstract

[The martingale approach to stochastic control is very natural and avoids some major mathematical difficulties that arise when Hamilton-Jacobi-Bellman partial differential equations are used to solve optimization problems. The brief history of stochastic control given here commences with the war effort in the US in the 1940s, proceeds through the 1950s and 1960s, and touches on more recent aspects. This history shows that the solution of problems in potential theory related to stochastic control and other stochastic filtering problems is an important mathematical manifestation of martingales.]

Published: Oct 18, 2022

Keywords: Martingale; Stochastic control

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