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Theory of Probability and Mathematical Statistics

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


Author: Iu. V. Ganychenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 23-41
MSC (2010): Primary 60J55; Secondary 60F17
DOI: https://doi.org/10.1090/tpms/947
Published electronically: August 6, 2015
MathSciNet review: 3241858
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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.


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Additional Information

Iu. V. Ganychenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Email: iurii_ganychenko@ukr.net

DOI: https://doi.org/10.1090/tpms/947
Keywords: Additive functionals, characteristic of an additive functional, $W$-measure, Markov approximation, diffusion process, local time, rate of convergence
Received by editor(s): April 25, 2013
Published electronically: August 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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