A note on weak convergence of random step processes

First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker and easier to check than the existing ones in the literature,...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2010-03, Vol.126 (4), p.381-395
Main Authors: Ispány, M., Pap, G.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker and easier to check than the existing ones in the literature, and they are derived from a very general semimartingale convergence theorem due to Jacod and Shiryaev, which is hard to use directly. Next, sufficient conditions are given for the convergence of stochastic integrals of random step functions, where the integrands are functionals of the integrators. This result covers situations which cannot be handled by existing ones.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-009-9099-5