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Stable convergence of semimartingales

Author

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  • Feigin, Paul D.

Abstract

Under a nesting condition on the sequence of histories, stable weak convergence of semimartingales to processes with conditionally independent increments is considered. Apart from ensuring the stability property, the nesting condition is more natural in some applications than an alternative measurability condition which appears in the literature.

Suggested Citation

  • Feigin, Paul D., 1985. "Stable convergence of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 125-134, February.
    • Handle: RePEc:eee:spapps:v:19:y:1985:i:1:p:125-134
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    Cited by:

    1. Crimaldi, Irene & Dai Pra, Paolo & Minelli, Ida Germana, 2016. "Fluctuation theorems for synchronization of interacting Pólya’s urns," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 930-947.
    2. van Zanten, Harry, 2000. "A multivariate central limit theorem for continuous local martingales," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 229-235, November.
    3. Giovanni Peccati & Murad S. Taqqu, 2008. "Stable Convergence of Multiple Wiener-Itô Integrals," Journal of Theoretical Probability, Springer, vol. 21(3), pages 527-570, September.
    4. Crimaldi, Irene & Pratelli, Luca, 2005. "Convergence results for multivariate martingales," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 571-577, April.
    5. Küchler, Uwe & Sørensen, Michael M., 1998. "A note on limit theorems for multivariate martingales," SFB 373 Discussion Papers 1998,45, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
    7. Teo Sharia, 2010. "Recursive parameter estimation: asymptotic expansion," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 343-362, April.

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