# Renormalization group of and convergence to the LISDLG process

ESAIM: Probability and Statistics (2004)

- Volume: 8, page 102-114
- ISSN: 1292-8100

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topIglói, Endre. "Renormalization group of and convergence to the LISDLG process." ESAIM: Probability and Statistics 8 (2004): 102-114. <http://eudml.org/doc/245404>.

@article{Iglói2004,

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.},

author = {Iglói, Endre},

journal = {ESAIM: Probability and Statistics},

keywords = {LISDLG process; dilative stability; renormalization group; functional limit theorem; regularly varying function},

language = {eng},

pages = {102-114},

publisher = {EDP-Sciences},

title = {Renormalization group of and convergence to the LISDLG process},

url = {http://eudml.org/doc/245404},

volume = {8},

year = {2004},

}

TY - JOUR

AU - Iglói, Endre

TI - Renormalization group of and convergence to the LISDLG process

JO - ESAIM: Probability and Statistics

PY - 2004

PB - EDP-Sciences

VL - 8

SP - 102

EP - 114

AB - 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.

LA - eng

KW - LISDLG process; dilative stability; renormalization group; functional limit theorem; regularly varying function

UR - http://eudml.org/doc/245404

ER -

## References

top- [1] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation. Cambridge University Press, Cambridge (1987). Zbl0617.26001MR898871
- [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. Zbl0397.60034
- [3] E. Iglói and G. Terdik, Superposition of diffusions with linear generator and its multifractal limit process. ESAIM: PS 7 (2003) 23–86. Zbl1017.60087
- [4] A.M. Iksanov and Z.J. Jurek, Shot noise distributions and selfdecomposability. Stoch. Anal. Appl. 21 (2003) 593–609. Zbl1042.60026
- [5] P.M. Lee, Infinitely divisible stochastic processes. Z. Wahrsch. Verw. Gebiete 7 (1967) 147–160. Zbl0167.46301
- [6] M.S. Taqqu, Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 (1979) 53–83. Zbl0397.60028

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