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Definition of the Stochastic Integral

  • K. L. Chung
  • R. J. Williams
Part of the Progress in Probability and Statistics book series (PRPR, volume 4)

Abstract

In this chapter, we shall define stochastic integrals of the form ∫[0, t] X dM where M is a right continuous local L 2-martingale and X is a process satisfying certain measurability and integrability assumptions, such that the family of stochastic integrals (∫[0, t] X dM, t ∈ ℝ+ is a right continuous local L 2-martingale. For certain M and X, the integral can be defined path-by-path.

Keywords

Continuous Path Continuous Version Stochastic Integral Predictable Process Predictable Time 
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.

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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • K. L. Chung
    • 1
  • R. J. Williams
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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