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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



An estimate of the rate of convergence of a sequence of additive functionals of difference approximations for a multidimensional diffusion process

Iu. V. Ganychenko

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Abstract: We consider a sequence of additive functionals of difference approximations for a multidimensional diffusion. A result by A. M. Kulik, Difference approximation for local times of multidimensional diffusions, Theory Probab. Math. Statist. 78 (2008), 67-83, on sufficient conditions for such a sequence to converge weakly to a W-functional of the limit process is improved. An estimate of the rate of convergence is obtained.

Keywords: Additive functionals, characteristic of an additive functional, W-measure, Markov approximation, diffusion process, local time, rate of convergence

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