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), 123134
MSC (2000):
Primary 60F17, 60G60
Published electronically:
August 12, 2005
MathSciNet review:
2109829
Fulltext PDF Free Access
Abstract 
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Abstract: Sufficient conditions for the tightness of a family of distributions of partial sum setindexed 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 finitedimensional distributions of the processes we obtain the invariance principle.
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 M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. MR 1102015 (93c:60001)
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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:
http://dx.doi.org/10.1090/S0094900005006368
PII:
S 00949000(05)006368
Received by editor(s):
February 27, 2003
Published electronically:
August 12, 2005
Additional Notes:
Supported in part by the RFFI grant 030100724.
Article copyright:
© Copyright 2005 American Mathematical Society
