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.
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
Brown, T.: A martingale approach to the Poisson convergence of simple point processes. Ann. Probab. 6, 615–628 (1978)
Dellacherie, C., Meyer, P.-A.: Probabilities and potential B. Amsterdam, New York, Oxford: North Holland 1982
Jacod, J., Mémin, J., Métivier, M.: On tightness and stopping times. Stochastic Process. Appl. 14, 109–146 (1983)
Kolmogorov, A.N., Fomin, S.V.: Introductory Real Analysis. Inglewood Cliff: Prentice Hall 1970
Schiopu-Kratina, I.: Tightness of pairs of càdlàg process. Stochastic Process Appl. 21, 167–177 (1985)
Schiopu-Kratina, I.: Weak convergence of processes in D(R) and compensation of point processes. Probab. Th. Rel. Fields 72, 99–109 (1986)
Author information
Authors and Affiliations
Rights and permissions
About this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00319985
Keywords
- Filtration
- Stochastic Process
- Probability Theory
- General Result
- Statistical Theory