A note on weak convergence of random step processes

Details A note on weak convergence of random step processes A note on weak convergence of random step processes

2007-01-28

arxiv.org/abs/math/0701803v2

Mathematics

Probability

9 pages long version of the first half of the original paper; to appear in Acta Mathematica Hungarica; some corrected typos

Scientific paper

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 convergence of stochastic integrals of random step functions, where the integrands are functionals of the integrators. This result covers situations which can not be handled by existing ones.

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