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Weak convergence of processes and preservation of predictability
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  • Published: October 1987

Weak convergence of processes and preservation of predictability

  • I. Schiopu-Kratina1 

Probability Theory and Related Fields volume 76, pages 231–241 (1987)Cite this article

Summary

This article investigates the preservation of predictability of a weakly converging sequence of increasing predictable processes. The convergence of compensators of submartingals to the compensator of a limiting submartingale is also considered. The general results are then applied to point processes. It is shown that in this case, with certain filtrations, only the weak convergence of point processes and their compensators is required to ensure that the limit of a sequence of compensators is the compensator of the limit.

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References

  • Aldous, D.J.: A new look at weak convergence. Talk given at the Ninth Conference on Stochastic Processes and Their Applications (1979)

  • Billingsley, P.: Convergence of probability measures. New York: Wiley 1968

    Google Scholar 

  • Brown, T.: A martingale approach to the Poisson convergence of simple point processes. Ann. Probab. 6, 615–628 (1978)

    Google Scholar 

  • Dellacherie, C., Meyer, P.-A.: Probabilities and potential B. Amsterdam, New York, Oxford: North Holland 1982

    Google Scholar 

  • Jacod, J., Mémin, J., Métivier, M.: On tightness and stopping times. Stochastic Process. Appl. 14, 109–146 (1983)

    Google Scholar 

  • Kolmogorov, A.N., Fomin, S.V.: Introductory Real Analysis. Inglewood Cliff: Prentice Hall 1970

    Google Scholar 

  • Schiopu-Kratina, I.: Tightness of pairs of càdlàg process. Stochastic Process Appl. 21, 167–177 (1985)

    Google Scholar 

  • Schiopu-Kratina, I.: Weak convergence of processes in D(R) and compensation of point processes. Probab. Th. Rel. Fields 72, 99–109 (1986)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Business Survey Methods Division, Statistics Canada, K1A 0T6, Ottawa, Canada

    I. Schiopu-Kratina

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  1. I. Schiopu-Kratina
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Cite this article

Schiopu-Kratina, I. Weak convergence of processes and preservation of predictability. Probab. Th. Rel. Fields 76, 231–241 (1987). https://doi.org/10.1007/BF00319985

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  • Received: 28 January 1986

  • Revised: 16 April 1987

  • Issue Date: October 1987

  • DOI: https://doi.org/10.1007/BF00319985

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Keywords

  • Filtration
  • Stochastic Process
  • Probability Theory
  • General Result
  • Statistical Theory
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