## 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
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### 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.
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