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1986•Advances in Applied ProbabilityRequires access

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

Anatole Joffe, Michel Métivier

Open publisher page 247 citations

Abstract

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 theD-semimartingales. Applications to multitype branching processes are given.

About this research paper

What this paper is about

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 theD-semimartingales. Applications to multitype branching processes are given.

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OpenAlex reports 247 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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 theD-semimartingales. Applications to multitype branching processes are given.

Key concepts: Semimartingale, Mathematics, Weak convergence, Branching (polymer chemistry), Convergence (economics), Applied mathematics, Martingale (probability theory), Stochastic process

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