Renormalization group of and convergence to the LISDLG process
ESAIM: Probability and Statistics, Tome 8 (2004), pp. 102-114.

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.

DOI : 10.1051/ps:2004006
Classification : 60F17, 60G10, 62M10
Mots clés : 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  - 
%0 Journal Article
%A Iglói, Endre
%T Renormalization group of and convergence to the LISDLG process
%J ESAIM: Probability and Statistics
%D 2004
%P 102-114
%V 8
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ps:2004006/
%R 10.1051/ps:2004006
%G en
%F PS_2004__8__102_0
Iglói, Endre. Renormalization group of and convergence to the LISDLG process. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 102-114. doi : 10.1051/ps:2004006. http://www.numdam.org/articles/10.1051/ps:2004006/

[1] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation. Cambridge University Press, Cambridge (1987). | MR | Zbl

[2] R.L. Dobrushin and P. Major, Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 (1979) 27-52. | Zbl

[3] E. Iglói and G. Terdik, Superposition of diffusions with linear generator and its multifractal limit process. ESAIM: PS 7 (2003) 23-86. | Numdam | Zbl

[4] A.M. Iksanov and Z.J. Jurek, Shot noise distributions and selfdecomposability. Stoch. Anal. Appl. 21 (2003) 593-609. | Zbl

[5] P.M. Lee, Infinitely divisible stochastic processes. Z. Wahrsch. Verw. Gebiete 7 (1967) 147-160. | Zbl

[6] M.S. Taqqu, Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 (1979) 53-83. | Zbl

Cité par Sources :