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

DOI:
https://doi.org/10.1090/S0094-9000-05-00636-8

Published electronically:
August 12, 2005

MathSciNet review:
2109829

Full-text PDF Free Access

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 , , exist. The dependence structure of the field is described by the -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

Email:
denis@orc.ru

DOI:
https://doi.org/10.1090/S0094-9000-05-00636-8

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