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Short Communications

On convergence in law of maxima of independent identically distributed random variables with random coefficients

A. N. Chuprunov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: This paper provides limit theorems for maxima of independent identically distributed random variables which belong to the domain of normal attraction of a max-stable variable and have random coefficients with the property of asymptotic negligibility or its analogues. The convergence of random step-functions determined by those maxima is studied in the Skorokhod space. The limit distributions are indicated.

Keywords: independent identically distributed random variables, convergence in law, functional limit theorem, invariance principle, max-stable distributions.

Received: 20.11.1996

DOI: 10.4213/tvp607

 English version: Theory of Probability and its Applications, 2000, 44:1, 93–97

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