Multifractal Analysis of Infinite Products of Stationary Jump Processes

Multifractal Analysis of Infinite Products of Stationary Jump Processes

There has been a growing interest in constructing stationary measures with known multifractal properties. In an earlier paper, the authors introduced the multifractal products of stochastic processes (MPSP) and provided basic properties concerning convergence, nondegeneracy, and scaling of moments....

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Main Authors: Petteri Mannersalo, Ilkka Norros, Rudolf H. Riedi
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2010/807491
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spelling doaj-bbcbe915ff2b475ba70f137b1f6ba23a2020-11-24T23:24:27ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/807491807491Multifractal Analysis of Infinite Products of Stationary Jump ProcessesPetteri Mannersalo0Ilkka Norros1Rudolf H. Riedi2VTT Technical Research Centre of Finland, P.O. Box 1100, 90571 Oulu, FinlandVTT Technical Research Centre of Finland, P.O. Box 1000, 02044 VTT, FinlandDepartment of Statistics, Rice University, MS 138, 6100 Main Street Houston, TX 77251-1892, USAThere has been a growing interest in constructing stationary measures with known multifractal properties. In an earlier paper, the authors introduced the multifractal products of stochastic processes (MPSP) and provided basic properties concerning convergence, nondegeneracy, and scaling of moments. This paper considers a subclass of MPSP which is determined by jump processes with i.i.d. exponentially distributed interjump times. Particularly, the information dimension and a multifractal spectrum of the MPSP are computed. As a side result it is shown that the random partitions imprinted naturally by a family of Poisson point processes are sufficient to determine the spectrum in this case.http://dx.doi.org/10.1155/2010/807491
collection DOAJ
language English
format Article
sources DOAJ
author Petteri Mannersalo
Ilkka Norros
Rudolf H. Riedi
spellingShingle Petteri Mannersalo
Ilkka Norros
Rudolf H. Riedi
Multifractal Analysis of Infinite Products of Stationary Jump Processes
Journal of Probability and Statistics
author_facet Petteri Mannersalo
Ilkka Norros
Rudolf H. Riedi
author_sort Petteri Mannersalo
title Multifractal Analysis of Infinite Products of Stationary Jump Processes
title_short Multifractal Analysis of Infinite Products of Stationary Jump Processes
title_full Multifractal Analysis of Infinite Products of Stationary Jump Processes
title_fullStr Multifractal Analysis of Infinite Products of Stationary Jump Processes
title_full_unstemmed Multifractal Analysis of Infinite Products of Stationary Jump Processes
title_sort multifractal analysis of infinite products of stationary jump processes
publisher Hindawi Limited
series Journal of Probability and Statistics
issn 1687-952X
1687-9538
publishDate 2010-01-01
description There has been a growing interest in constructing stationary measures with known multifractal properties. In an earlier paper, the authors introduced the multifractal products of stochastic processes (MPSP) and provided basic properties concerning convergence, nondegeneracy, and scaling of moments. This paper considers a subclass of MPSP which is determined by jump processes with i.i.d. exponentially distributed interjump times. Particularly, the information dimension and a multifractal spectrum of the MPSP are computed. As a side result it is shown that the random partitions imprinted naturally by a family of Poisson point processes are sufficient to determine the spectrum in this case.
url http://dx.doi.org/10.1155/2010/807491
work_keys_str_mv AT petterimannersalo multifractalanalysisofinfiniteproductsofstationaryjumpprocesses
AT ilkkanorros multifractalanalysisofinfiniteproductsofstationaryjumpprocesses
AT rudolfhriedi multifractalanalysisofinfiniteproductsofstationaryjumpprocesses
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