Hiroshima Mathematical Journal

$S\alpha S\;M(t)$-processes and their canonical representations

Katsuya Kojo

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 23, Number 2 (1993), 305-326.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206128254

Digital Object Identifier
doi:10.32917/hmj/1206128254

Mathematical Reviews number (MathSciNet)
MR1228573

Zentralblatt MATH identifier
0785.60012

Subjects
Primary: 60G18: Self-similar processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions

Citation

Kojo, Katsuya. $S\alpha S\;M(t)$-processes and their canonical representations. Hiroshima Math. J. 23 (1993), no. 2, 305--326. doi:10.32917/hmj/1206128254. https://projecteuclid.org/euclid.hmj/1206128254


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References

  • [1] S. Cambanis, C. D. Hardin Jr. and A. Weron, Innovations and Wold Decompositions of Stable Sequences, Probab. Theory Related Fields, 79 (1988), 1-27.
  • [2] N. N. Chentsov, Levy's Brownian motion of several parameters and generalized white noise, Theory Probab. Appl., 2 (1957), 265-266.
  • [3] T. Hida, Canonical representations of Gaussian processes and their applications, Mem. Coll. Sci. Univ. Kyoto, Ser. A. Math., 33 (1960), 109-155.
  • [4] T. Hida and N. Ikeda, Note on linear processes, J. Math. Kyoto Univ., 1 No. 1 (1961), 75-86.
  • [5] K. Ito, Probability Theory (in Japanese), Iwanami, Tokyo, 1978.
  • [6] K. Kojo and S. Takenaka, On Canonical Representations of Stable M(t)-processes, to appear in Probab. Math. Statist., 13 fasc. 2.
  • [7] J. Kuelbs, A Representation Theorem for Symmetric Stable Processes and Stable Measures on H, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 26 (1973), 259-271.
  • [8] P. Levy, Fonctions aleatoires a correlation lineaire, Illinois J. Math., 1 (1957), 217-258.
  • [9] H. P. McKean Jr., Brownian Motion with a Several-Dimensional Time, Theory Probab. Appl., 8 (1963), 335-354.
  • [10] T. Mori, Representation of linearly additive random fields, Probab. Theory Related Fields, 92 (1992), 91-115.
  • [11] J. Rosinski, On path properties of certain infinitely divisible processes, Stochastic Process. Appl., 33 (1989), 73-87.
  • [12] K. Sato, Infinitely divisible distributions (in Japanese), Seminar on Probab., 52 (1981).
  • [13] M. Schilder, Some Structure Theorems for the Symmetric Stable Laws, Ann. Math.Statist., 41 No. 2 (1970), 412-421.
  • [14] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, 1970.
  • [15] K. Takashima, Sample path properties of ergodic self-similar processes, Osaka J. Math., 26 (1989), 159-189.
  • [16] S. Takenaka, Integral-geometric construction of self-similar stable processes, Nagoya Math. J., 123 (1991), 1-12.
  • [17] S. Takenaka, I. Kubo and H. Urakawa, Brownian motion parametrized with metric space of constant curvature, Nagoya Math. J., 82 (1981), 131-140.
  • [18] N. J. Vilenkin, Special Functions and the Theory of Group Representations, Trans. Math. Monographs, 22 (1968).
  • [19] A. Weron, Stable processes and measures; a survey, Probab. Theory on Vector Spaces III, Lecture Notes in Math., Springer-Verlag, 1080 (1983), 306-364.