Renormalization group of and convergence to the LISDLG process

Endre Iglói

ESAIM: Probability and Statistics (2004)

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

Abstract

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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.

How to cite

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Iglói, 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

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  1. [1] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation. Cambridge University Press, Cambridge (1987). Zbl0617.26001MR898871
  2. [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. [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. [4] A.M. Iksanov and Z.J. Jurek, Shot noise distributions and selfdecomposability. Stoch. Anal. Appl. 21 (2003) 593–609. Zbl1042.60026
  5. [5] P.M. Lee, Infinitely divisible stochastic processes. Z. Wahrsch. Verw. Gebiete 7 (1967) 147–160. Zbl0167.46301
  6. [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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