Linearly additive random fields with independent increments on time like curves

• Autorzy: Takenaka S.
• Języki publikacji: EN

Abstrakty

EN

Let V be a convex cone in Rⁿ. A curve L = {l(t); t ∈ R₊} ⊂ Rⁿ is called a time-like curve if {l(s); s ≥ t} ⊂ l(t) + V holds for any t. A random field {X(t); t ∈ Rⁿ} whose restriction X|_L(t) = X (l(t)) on time-like curve L becomes an additive process is considered and it is characterized as a set-indexed random field on the dual cone V^∗.

Słowa kluczowe

EN

random fields; linearly additive random fields; convex cone

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 1
• Strony: 1--5
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Takenaka S.

• Department of Applied Mathematics, Okayama University of Science, 700-0005, Okayama, Japan

Bibliografia

• [1] K. Kojo and S. Takenaka, On canonical representations of stable Mt-processes, Probab. Math. Statist 13 (1992), pp. 229-238.
• [2] T. Mori, Representation of linearly additive random fields, Probab. Theory Related Fields 92 (1992), pp. 91-115.
• [3] A. Rocha-Arteaga and K. Sato, Topics in Infinitely Divisible Distributions and Lévy Processes, Communicación Técnica No 1-01-15/15-08-2001 (2001).
• [4] Y. Sato, Distributions of stable random fields of Chentsov type, Nagoya Math. J. 123 (1991), pp. 119-139.
• [5] Y. Sato, Structure of Lévy measures of stable random fields of Chentsov type, Probab. Math. Statist. 13 (1992), pp. 165-176.
• [6] Y. Sato and S. Takenaka, On determinism of symmetric α-stable processes of generalized Chentsov type, in: Gaussian Random Fields, World Scientific, 1991, pp. 332-345.
• [7] S. Takenaka, Representations of Euclidean random field, Nagoya Math. J. 105 (1987), pp. 19-31.
• [8] S. Takenaka, Integral-geometric constructions of self-similar stable processes, Nagoya Math. J. 123 (1991), pp. 1-12.
• [9] S. Takenaka, Examples of self-similar stable processes, in: Stochastic Processes, Springer, 1993, pp. 303-311.
• [10] S. Takenaka, On determinism of set-indexed SαS-processes, in: Trends in Probability and Related Analysis 1999, World Scientific, 1999, pp. 285-290.
• [11] S. Takenaka, On Set-Indexed Processes (in Japanese), Bulletin of Okayama Univ. of Science 37A (2002), pp. 15-21.
• [12] S. Takenaka, Linearly additive random fields with independent increments on time-like curves, in: Problems on Infinitely Divisible Processes (6), Cooperative research report, Institute of Statistical Mathematics 146 (2002), pp. 13-19.