Martingale Theory

  • John Lamperti
Part of the Applied Mathematical Sciences book series (AMS, volume 23)


Suppose that a gambler places bets at discrete times t = 1,2,..., and that his fortune after the n’th bet is the random variable Xn. (Thus X 0 is the initial stake, and in general the Xn’s can take positive or negative real values.) How can we express the idea that the sequence of bets is “fair”?


Convergence Theorem Martingale Theory Fair Game Integrable Random Variable Hand Limit 
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  1. J. L. Snell (1952): “Applications of martingale system theorems,” Trans. Am. Math. Soc. 73, pp. 293–312.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • John Lamperti
    • 1
  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

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