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Difference approximation for local times of multidimensional diffusions

Alexey M. Kulik
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Abstract

We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the limiting process. The class of the W-functionals, that can be obtained as the limiting ones, is completely described in the terms of the associated W-measures, and coincides with the class of the functionals that are regular w.r.t. the phase variable.

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Alexey M. Kulik. 2007-04-04. Difference approximation for local times of multidimensional diffusions. https://arxiv.org/abs/math/0702175

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