Journal of Statistical Planning and Inference 133 (2005) 159 – 172 www.elsevier.com/locate/jspi Normalizing constants for record values in Archimedean copula processes  A. Berred a , ∗ , V.B. Nevzorov b , S. Wey a a Laboratoire de Mathematiques Appliquees, BP 540, 25 rue Philippe Lebon, Le Havre Cedex 76058, France b Department of Mathematics and Mechanics, St. Petersburg State University, 2 Bibliotechnaya Sq., 198504, St. Petersburg, Russia Received 14 January 2003; accepted 8 March 2004 Available online 9 June 2004 Abstract In this paper, we detail an asymptotic behavior of record values for some types of Archimedean copula processes, refining the form of the corresponding normalizing constants. © 2004 Published by Elsevier B.V. MSC: Primary 62E20; Secondary 62G20,62G30 Keywords: Archimedean copula process; Extremes; Record times; Record values 1. Introduction Let X 1 ,X 2 ,... be a sequence of random variables (r.v.’s) and M(n) = max{X 1 ,...,X n } for n=1, 2,... . We define (upper) record times L(n), (upper) record values X(n) and record indicators  n as follows: L(1) = 1, L(n + 1) = min{j : X j >X L(n) },n = 1, 2,..., X(n) = X L(n) = M(L(n)), n = 1, 2,...,  1 = 1,  n = 1 {M(n)>M(n-1)} ,n = 2, 3, ... .  This work was partially supported by Russian Foundation of Basic Research (Grant 01-01-00031 and 02-01- 01099). ∗ Corresponding author. Tel.: +33-232-744322; fax: +33-232-744314. E-mail address: alexandre.berred@univ-lehavre.fr (A. Berred) 0378-3758/$ - see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.jspi.2004.03.006