Square integrable martingales, and structure of the functionals on a Wiener process

  • R. S. Liptser
  • A. N. Shiryayev
Part of the Applications of Mathematics book series (SMAP, volume 5)


Let (Ω, ℱ, P) be a complete probability space, and let F = (ℱ t ), t ≥ 0, be a nondecreasing (right continuous) family of sub-σ-algebras ℱ, each of which is augmented by sets from ℱ having zero P-probability.


Conditional Expectation Continuous Modification Simple Function Wiener Process Diffusion Type 


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Notes and references

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    Yershov M. P., Sequential estimation of diffusion processes. Teoria Verojatn. i Primenen. XV, 4 (1970), 705–717.Google Scholar
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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • R. S. Liptser
    • 1
  • A. N. Shiryayev
    • 2
  1. 1.Institute for Problems of Control TheoryMoscowUSSR
  2. 2.Institute of Control SciencesMoscowUSSR

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