Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-03T09:02:15.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Renormalization group of and convergence to the LISDLG process

Published online by Cambridge University Press:  15 September 2004

Endre Iglói
Endre Iglói*
Affiliation:
Institute of Informatics, University of Debrecen, 4010 Debrecen, PF 12, Hungary; [email protected].
Get access

Abstract

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.

Keywords

LISDLG processdilative stabilityrenormalization groupfunctional limittheoremregularly varying function.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 102 - 114
Copyright
© EDP Sciences, SMAI, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation. Cambridge University Press, Cambridge (1987).
Dobrushin, R.L. and Major, P., Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 (1979) 27–52. CrossRef
Iglói, E. and Terdik, G., Superposition of diffusions with linear generator and its multifractal limit process. ESAIM: PS 7 (2003) 23–86. CrossRef
Iksanov, A.M. and Jurek, Z.J., Shot noise distributions and selfdecomposability. Stoch. Anal. Appl. 21 (2003) 593–609. CrossRef
Lee, P.M., Infinitely divisible stochastic processes. Z. Wahrsch. Verw. Gebiete 7 (1967) 147–160. CrossRef
Taqqu, M.S., Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 (1979) 53–83. CrossRef