 Stationary self-similar random fields on the integer latticeZhiyi Chi Stochastic Processes and their Applications, 2001, vol. 91, issue 1, 99-113 Abstract: We establish several methods for constructing stationary self-similar random fields (ssf's) on the integer lattice by "random wavelet expansion", which stands for representation of random fields by sums of randomly scaled and translated functions, or more generally, by composites of random functionals and deterministic wavelet expansion. To construct ssf's on the integer lattice, random wavelet expansion is applied to the indicator functions of unit cubes at integer sites. We demonstrate how to construct Gaussian, symmetric stable, and Poisson ssf's by random wavelet expansion with mother wavelets having compact support or non-compact support. We also generalize ssf's to stationary random fields which are invariant under independent scaling along different coordinate axes. Finally, we investigate the construction of ssf's by combining wavelet expansion and multiple stochastic integrals. Keywords: Stationary; self-similar; Random; wavelet; expansion; Multiple; stochastic; integral; Invariance; under; independent; scaling (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:91:y:2001:i:1:p:99-113 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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