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Weak convergence of processes in D(R) and compensation of point processes
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  • Published: April 1986

Weak convergence of processes in D(R) and compensation of point processes

  • I. Schiopu-Kratina1 

Probability Theory and Related Fields volume 72, pages 99–109 (1986)Cite this article

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Summary

Real valued càdlàg processes are viewed in the manner described in [2], as random elements of D(R) which is endowed with the J 1 topology. We consider a sequence of point processes (N n, \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathfrak{F}}\) n* , ℱ, P) n≧1 with their minimal filtrations, together with their compensators A n, \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathfrak{F}}\) n* , ℱ, P) n≧1. Under slightly stronger assumptions than N n⇒N and A n⇒A, we show that A has the same distribution in D(R) as the compensator of N for the filtration generated by N and A.

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References

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

  2. Billingsley, P.: Convergence of Probability Measures. New York: Wiley 1968

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Authors and Affiliations

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

    I. Schiopu-Kratina

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  1. I. Schiopu-Kratina
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Schiopu-Kratina, I. Weak convergence of processes in D(R) and compensation of point processes. Probab. Th. Rel. Fields 72, 99–109 (1986). https://doi.org/10.1007/BF00343898

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  • Received: 12 June 1984

  • Revised: 22 September 1985

  • Issue Date: April 1986

  • DOI: https://doi.org/10.1007/BF00343898

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Keywords

  • Filtration
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Point Process
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