Random point processes: Stieltjes stochastic integrals

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


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).


Poisson Process Point Process Stochastic Integral Minimal Representation Local Martingale 
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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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