Semimartingales and Stochastic Integrals

  • Philip E. Protter
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 21)


The purpose of the theory of stochastic integration is to give a reasonable meaning to the idea of a differential to as wide a class of stochastic processes as possible. We saw in Sect. 8 of Chap. I that using Stieltjes integration on a path-by-path basis excludes such fundamental processes as Brownian motion, and martingales in general. Markov processes also in general have paths of unbounded variation and are similarly excluded. Therefore we must find an approach more general than Stieltjes integration.


Brownian Motion Variable Formula Quadratic Variation Standard Brownian Motion Continuous Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Philip E. Protter
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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