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Renormalization group of and convergence to the LISDLG process. (English) Zbl 1154.60322

Summary: The LISDLG process denoted by \(J(t)\) is defined in the author and G. Terdik [ESAIM, Probab. Stat. 7, 23–88 (2003; Zbl 1017.60087) 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.

MSC:

60F17 Functional limit theorems; invariance principles
60G10 Stationary stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Citations:

Zbl 1017.60087
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References:

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