Random point processes: Stieltjes stochastic integrals

  • R. S. Liptser
  • A. N. Shiryayev
Part of the Applications of Mathematics book series (SMAP, volume 6)

Abstract

In the previous chapters we described observable random processes X = (ξ t ), t ≥ 0, which possessed continuous trajectories and had properties analogous, to a certain extent, to those of a Wiener process. Chapters 18 and 19 will deal with the case of an observable process that is a point process whose trajectories are pure jump functions (a Poisson process with constant or variable intensity is a typical example).

Keywords

Poisson Process Point Process Stochastic Integral Minimal Representation Local Martingale 
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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Notes and references

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Copyright information

© Springer Science+Business Media New York 1978

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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