SFB 303 Discussion Paper No. B-253
Author:
Evstigneev, Igor V., and Klaus Schürger
Title: A Limit Theorem for Random Matrices with a Multiparameter and
It's Application to a Stochastic Model of a Large Economy
Abstract: Based on multiparameter subadditive ergodic theorems of Akcoglu and Krengel
(1981) and Schürger (1988) we derive an almost sure limit theorem for
families of random matrices with a multiparameter which satisfy a
supermultiplicativity condition. This gives a multiparameter analogue
of results of Fürstenberg and Kesten (1960) and Klingman (1973, 1976)
(note, however, that our supermultiplicativity assumption is more restrictive
since it involves products in an arbitrary order). It turns out that a Borel-Cantelli
argument in Kingman (1973, 1976) has to be replaced by a projection argument
involving subadditive processes with lower dimensional indices. Finally, we outline
how our main convergence result applies to a certain stochastic model of a
large economy.
Keywords: law of large numbers, products of random matrices, subadditive processes,
ergodic theory, stochastic economy growth model
JEL-Classification-Number:
111, 213
Creation-Date: 12.8.1993
Unfortunately this paper is not available. Please order a hardcopy via e-mail.
17.02.1998, © Webmaster
