The LISDLG process denoted by J(t) is defined in Iglói and Terdik [ESAIM: PS7 (2003) 23–86] by afunctional limit theorem as the limit of ISDLG processes. This paper gives amore 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 thelimit process of the renormalization operator flow applied to the elements ofsome set of stochastic processes. The latter set consists of IGSDLG processeswhich are generalizations of the ISDLG process.