Itô Integration

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


The Itô integral carries the notion of a martingale transform from discrete time into continuous time. The construction gives us a systematic method for building new martingales, and it leads to a new calculus for stochastic processes, the consequences of which turn out to be more far reaching than anyone could have possibly expected. The Itô calculus is now well established as one of the most useful tools of probability theory.


Triangle Inequality Cauchy Sequence Dense Subset Integral Sign Approximation Theorem 
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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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