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Weak convergence of sequences of semimartingales with applications to multitype branching processes

  • A. Joffe (a1) and M. Metivier (a2)


The paper is devoted to a systematic discussion of recently developed techniques for the study of weak convergence of sequences of stochastic processes. The methods described make essential use of the semimartingale structure of the processes. Sufficient conditions for tightness including the results of Rebolledo are derived. The techniques are applied to a special class of processes, namely the D-semimartingales. Applications to multitype branching processes are given.


Corresponding author

Postal address: Département de Mathématiques et Statistique, Université de Montréal, P.O. Box 6128, Succ. A, Montréal, Québec H3C 3J7, Canada.
∗∗Postal address: Centre de Mathématiques Appliquées, École Polytechnique, Cedex 91128, Palaiseau, France.


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Research supported in part by the Natural Science and Engineering Research Council, Canada, the FCAC Programme of the Ministère de l'Education du Québec, and the Air Force Office of Scientific Research Grant No. F49620–82-C-0009, USA.



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Weak convergence of sequences of semimartingales with applications to multitype branching processes

  • A. Joffe (a1) and M. Metivier (a2)


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