×

Decomposition of stationary \(\alpha\)-stable random fields. (English) Zbl 1044.60039

Summary: This work is concerned with the structural analysis of stationary \(\alpha\)-stable random fields. Three distinct classes of such random fields are characterized and it is shown that every stationary \(\alpha\)-stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes. Various examples of stationary \(\alpha\)-stable random fields are discussed in this context.

MSC:

60G60 Random fields
60G52 Stable stochastic processes
60G57 Random measures
60E07 Infinitely divisible distributions; stable distributions
60G10 Stationary stochastic processes
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Gross, A. and Weron, A. (1994). On measure-preserving transformations and doubly stationary symmetric stable processes. Studia Math. 114 275-287. · Zbl 0829.60029
[2] Janicki, A. and Weron, A. (1994). Simulation and Chaotic Behavior of -stable Stochastic Processes. Dekker, New York. · Zbl 0946.60028
[3] Kallenberg, O. (1975). Random Measures. Springer, New York. · Zbl 0296.60020
[4] Krengel, U. (1969). Darstellungssätze f ür strömungen und halbströmungen. I. Math. Ann. 182 1-39. · Zbl 0167.32801
[5] Rosi ński, J. (1994). On the uniqueness of the spectral representation of stable processes. J. Theoret. Probab. 7 615-634. · Zbl 0805.60030
[6] Rosi ński, J. (1995). On the structure of stationary stable processes. Ann. Probab. 23 1163-1187. · Zbl 0836.60038
[7] Samorodnitsky, G. and Taqqu, M. S. (1994). Non-Gaussian Stable Processes. Chapman and Hall, London. · Zbl 0925.60027
[8] Surgailis, D., Rosi ński, J., Mandrekar, V. and Cambanis, S. (1993). Stable mixed moving averages. Probab. Theory Related Fields 97 543-558. · Zbl 0794.60026
[9] Varadarajan, V. S. (1970). Geometry of Quantum Theory 2. Van Nostrand Reinhold, New York. · Zbl 0194.28802
[10] ziemmer, R. J. (1984). Ergodic Theory and Semisimple Groups. Birkhäuser. Boston.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.