First Martingale Steps

  • J. Michael Steele
Part of the Applications of Mathematics book series (SMAP, volume 45)


The theory of martingales began life with the aim of providing insight into the apparent impossibility of making money by placing bets on fair games. The success of the theory has far outstripped its origins, and martingale theory is now one of the main tools in the study of random processes. The aim of this chapter is to introduce the most intuitive features of martingales while minimizing formalities and technical details. A few definitions given here will be refined later, but the redundancy is modest, and the future abstractions should go down more easily with the knowledge that they serve an honest purpose.


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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • J. Michael Steele
    • 1
  1. 1.The Wharton School, Department of StatisticsUniversity of PennsylvaniaPhiladelphiaUSA

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