Theory of Probability and Mathematical Statistics

Author(s): D. V. Poryvai
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 70 (2004).
Journal: Theor. Probability and Math. Statist. No. 70 (2005), 123-134.
MSC (2000): Primary 60F17, 60G60
Posted: August 12, 2005
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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 $\beta_1$ -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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D. V. Poryvai
Affiliation: Department of Probability Theory, Mechanics and Mathematics Faculty, Moscow State University, Moscow, Russia
Email: denis@orc.ru

DOI: 10.1090/S0094-9000-05-00636-8
PII: S 0094-9000(05)00636-8
Received by editor(s): 27/FEB/2003
Posted: August 12, 2005
Additional Notes: Supported in part by the RFFI grant 03-01-00724.
Copyright of article: Copyright 2005, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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