Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

Iglói, Endre; Terdik, György

doi:10.1051/ps:2003008

Cited by 18 publications

(19 citation statements)

References 38 publications

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“…The construction of the GSDLG (General SDLG) process is similar to that of the SDLG process (see [3], Sect. 3.1), that is superposition of stationary DLG processes with properly chosen random parameters.…”

Section: Gsdlg Processesmentioning

confidence: 99%

“…, m), and τ 0 is the identity permutation. The LISDLG process has the remarkable property called dilative stability (see [3], Def. 3 and Th.…”

Section: The Renormalization Group Of the Lisdlg Processmentioning

confidence: 99%

“…Recall that the LISDLG process {J(t), t ≥ 0} can be defined as the a.s. (almost surerely) continuous process which has a zero mean and the following second and higher order joint cumulants (see [3], Prop. 14): (2, 3, .…”

Section: The Renormalization Group Of the Lisdlg Processmentioning

confidence: 99%

“…These are the processes from which we derive the above mentioned IGSDLG processes, by taking the integral and adjusting the mean to zero. The construction of a GSDLG process is similar to that of an SDLG process (see [3], Sect. 3.1), that is superposition of independent (conditionally on the sequence of random parameters −2α k ) stationary DLG processes with properly chosen random parameters.…”

Section: Introductionmentioning

confidence: 99%

“…This paper can be considered to be the supplement of [3] insomuch as it is built upon the results of that paper. So the DLG, SDLG and LISDLG processes are supposed to be known to the reader.…”

Section: Introductionmentioning

confidence: 99%

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Renormalization group of and convergence to the LISDLG process

Iglói

2004

ESAIM: PS

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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.Mathematics Subject Classification. 60F17, 60G10, 62M10.

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Section: Gsdlg Processesmentioning

confidence: 99%

“…, m), and τ 0 is the identity permutation. The LISDLG process has the remarkable property called dilative stability (see [3], Def. 3 and Th.…”

Section: The Renormalization Group Of the Lisdlg Processmentioning

confidence: 99%

Section: The Renormalization Group Of the Lisdlg Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%