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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 -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