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A Criterion of Convergence of Generalized Processes and an Application to a Supercritical Branching Particle System

Published online by Cambridge University Press:  20 November 2018

Begoña Fernández  and
Luis G. Gorostiza
Begoña Fernández
Affiliation:
Facultad de Ciencias, UNAM, México 04510, D.F. México
Luis G. Gorostiza
Affiliation:
Centro de Investigación y de Estudios Avanzados, México 07300, D.F. México
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The problem of convergence in distribution of a large class of generalized semimartingales to a continuous process is considerably simplified by a recent theorem of Aldous [1], in conjunction with a result of Cremers and Kadelka [3] on convergence of integral functional, and the results of Mitoma [15] and Fouque [8] for generalized processes. We will give a convenient convergence criterion in this setting. The proof amounts to a direct combination of the results of the abovementioned authors, requiring only a minor extension (of a special case) of the theorem of Cremers and Kadelka.

Keywords

60F1760G2060J80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 985 - 997
Copyright
Copyright © Canadian Mathematical Society 1991

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