The LISDLG process denoted by $J\left(t\right)$ 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 $J\left(t\right)$. It is shown that process $J\left(t\right)$ has its own renormalization group and that $J\left(t\right)$ 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.

Keywords: LISDLG process, dilative stability, renormalization group, functional limit theorem, regularly varying function

@article{PS_2004__8__102_0, author = {Igl\'oi, Endre}, title = {Renormalization group of and convergence to the {LISDLG} process}, journal = {ESAIM: Probability and Statistics}, pages = {102--114}, publisher = {EDP-Sciences}, volume = {8}, year = {2004}, doi = {10.1051/ps:2004006}, mrnumber = {2085609}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2004006/} }

TY - JOUR AU - Iglói, Endre TI - Renormalization group of and convergence to the LISDLG process JO - ESAIM: Probability and Statistics PY - 2004 SP - 102 EP - 114 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2004006/ DO - 10.1051/ps:2004006 LA - en ID - PS_2004__8__102_0 ER -

Iglói, Endre. Renormalization group of and convergence to the LISDLG process. ESAIM: Probability and Statistics, Volume 8 (2004), pp. 102-114. doi : 10.1051/ps:2004006. http://www.numdam.org/articles/10.1051/ps:2004006/

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