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1995 | 115 | 2 | 109-127
Tytuł artykułu

Chaotic behavior of infinitely divisible processes

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EN
Abstrakty
EN
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
Twórcy
autor
  • Department of Statistics, University of North Carolina, Chapel Hill, North Carolina 27599-3260, U.S.A., , cambanis@stat.unc.edu
autor
Bibliografia
  • R. J. Adler, S. Cambanis and G. Samorodnitsky (1990), On stable Markov processes, Stochastic Process. Appl. 34, 1-17.
  • R. M. Blumenthal (1957), An extended Markov property, Trans. Amer. Math. Soc. 85, 52-72.
  • S. Cambanis, C. D. Hardin and A. Weron (1987), Ergodic properties of stationary stable processes, Stochastic Process. Appl. 24, 1-18.
  • S. Cambanis and A. Ławniczak (1989), Ergodicity and mixing of infinitely divisible processes, unpublished preprint.
  • I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai (1982), Ergodic Theory, Springer, Berlin.
  • S. V. Fomin (1950), Normal dynamical systems, Ukrain. Mat. Zh. 2, 25-47 (in Russian).
  • U. Grenander (1950), Stochastic processes and statistical inference, Ark. Mat. 1, 195-277.
  • A. Gross (1994), Some mixing conditions for stationary symmetric stable stochastic processes, Stochastic Process. Appl. 51, 277-285.
  • A. Gross and J. B. Robertson (1993), Ergodic properties of random measures on stationary sequences of sets, ibid. 46, 249-265.
  • M. Hernández and C. Houdré (1993), Disjointness results for some classes of stable processes, Studia Math. 105 235-252.
  • P. Kokoszka and K. Podgórski (1992), Ergodicity and weak mixing of semistable processes, Probab. Math. Statist. 13, 239-244.
  • A. Lasota and M. C. Mackey (1994), Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Springer, New York.
  • V. P. Leonov (1960), The use of the characteristic functional and semiinvariants in the theory of stationary processes, Dokl. Akad. Nauk SSSR 133, 523-526 (in Russian).
  • G. Maruyama (1949), The harmonic analysis of stationary stochastic processes, Mem. Fac. Sci. Kyusyu Ser. Mat. IV 1, 49-106.
  • G. Maruyama (1970), Infinitely divisible processes, Probab. Theory Appl. 15, 3-23.
  • J. Musielak (1983), Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, New York. D. Newton (1968), On a principal factor system of a normal dynamical system, J. London Math. Soc. 43, 275-279.
  • K. Podgórski (1992), A note on ergodic symmetric stable processes, Stochastic Process. Appl. 43, 355-362.
  • K. Podgórski and A. Weron (1991), Characterization of ergodic stable processes via the dynamical functional, in: Stable Processes and Related Topics, S. Cambanis et al. (eds.), Birkhäuser, Boston, 317-328.
  • B. S. Rajput and J. Rosiński (1989), Spectral representations of infinitely divisible processes, Probab. Theory Related Fields 82, 451-487.
  • V. A. Rokhlin (1964), Exact endomorphisms of Lebesgue space, Amer. Math. Soc. Transl. (2) 39, 1-36.
  • P. Walters (1982), An Introduction to Ergodic Theory, Springer, Berlin.
  • A. Weron (1985), Harmonizable stable processes on groups: spectral, ergodic and interpolation properties, Z. Wahrsch. Verw. Gebiete 68, 473-491.
Typ dokumentu
Bibliografia
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