Renormalization group of and convergence to the LISDLG process

Institute of Informatics, University of Debrecen, 4010 Debrecen, PF 12, Hungary; igloi@inf.unideb.hu.

Received: 15 January 2003
Revised: 19 February 2004

Abstract

The LISDLG process denoted by J(t) is defined in Iglói and Terdik [ESAIM: PS 7 (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of J(t). It is shown that process J(t) has its own renormalization group and that J(t) can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations of the ISDLG process.