• Kenneth Lange
Part of the Springer Texts in Statistics book series (STS, volume 0)


Martingales generalize the notion of a fair game in gambling. Theory to the contrary, many gamblers still believe that they simply need to hone their strategies to beat the house. Probabilists know better. The real payoff with martingales is their practical value throughout probability theory. This chapter introduces martingales, develops some relevant theory, and delves into a few applications. As a prelude, readers are urged to review the material on conditional expectations in Chapter 1. In the current chapter we briefly touch on the convergence properties of martingales, the optional stopping theorem, and large deviation bounds via Azuma’s inequality. More extensive treatments of martingale theory appear in the books [23, 24, 53, 80, 106, 118, 208]. Our other referenced sources either provide elementary accounts comparable in difficulty to the current material [129, 170] or interesting special applications [4, 134, 186, 201].


Independent Random Variable Fractional Linear Transformation Bernoulli Random Variable Longe Common Subsequence Martingale Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and StatisticsUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations