Asymptotic behavior of increments of random fields
Author:
O. E. Shcherbakova
Translated by:
The author
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal:
Theor. Probability and Math. Statist. 68 (2004), 173186
MSC (2000):
Primary 60F15; Secondary 60K05
Published electronically:
May 25, 2004
MathSciNet review:
2000647
Fulltext PDF Free Access
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Abstract: Some results on the asymptotic behavior of increments of a dimensional random field are proved. Let and be fixed and let be the maximum increment of a dimensional random field of independent identically distributed random variables evaluated for dimensional rectangles such that and . Denote also by the maximum increment evaluated for rectangles such that . We determine the asymptotic almost sure behavior of random variables and . Steinebach (1983) proved a similar result for the case of rectangles belonging to the cube (of volume ) and under the condition that as for all . Note that the sequence is monotone in this case. We also consider the cases where or .
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Additional Information
O. E. Shcherbakova
Affiliation:
Chair of Mathematics, Department of Physics and Mechanics, St. Petersburg State Technical University, Politekhnitcheskaya Street 29, St. Petersburg 195251, Russia
Email:
helgagold_@pochtamt.ru, helga_scher@mailru.com
DOI:
http://dx.doi.org/10.1090/S009490000400599X
PII:
S 00949000(04)00599X
Received by editor(s):
April 4, 2002
Published electronically:
May 25, 2004
Additional Notes:
Supported in part by the Ministry of Education of the Russian Federation under grants N E001.082 and “Leading scientific school” # 001596019.
Article copyright:
© Copyright 2004 American Mathematical Society
