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Theory of Probability and Mathematical Statistics

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The invariance principle for a class of dependent random fields

Author: D. V. Poryvai
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 123-134
MSC (2000): Primary 60F17, 60G60
Published electronically: August 12, 2005
MathSciNet review: 2109829
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Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions for the tightness of a family of distributions of partial sum set-indexed processes constructed from symmetric random fields are obtained in this paper. We require that the moments of order $s$, $s>2$, exist. The dependence structure of the field is described by the $\beta_1$-mixing coefficients decreasing with a power rate. Assuming that a field is stationary and applying a result of D. Chen (1991) on the convergence of finite-dimensional distributions of the processes we obtain the invariance principle.

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Additional Information

D. V. Poryvai
Affiliation: Department of Probability Theory, Mechanics and Mathematics Faculty, Moscow State University, Moscow, Russia

Received by editor(s): February 27, 2003
Published electronically: August 12, 2005
Additional Notes: Supported in part by the RFFI grant 03-01-00724.
Article copyright: © Copyright 2005 American Mathematical Society