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On the determinism of the distributions of multiple Markov non-Gaussian symmetric stable processes

Published online by Cambridge University Press:  22 January 2016

Katsuya Kojo
Katsuya Kojo*
Affiliation:
Niihama National College of Technology, Niihama 792, Japan
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Abstract.

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Consider a non-Gaussian SαS process X = {X(t); t ∈ T} which is expressed as a canonical representation , and is continuous in probability. If X is n-ple Markov, then X has determinism of dimension n + 1. That is, any SαS process having the same (n + l)-dimensional distributions with X is identical in law with X.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 150 , June 1998 , pp. 177 - 196
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Hida, T., Canonical representation of Gaussian processes and their applications, Mem. Col. Sci. Univ. Kyoto, Ser. A, 33 (1960), 109–155.Google Scholar
[2] Kojo, K., SαS M (t)-processes and their canonical representations, Hiroshima Math. J., 23 (1993), 305–326.CrossRefGoogle Scholar
[3] Kojo, K., On the notion of multiple Markov SαS processes, Hiroshima Math. J., 25 (1995), 143–157.CrossRefGoogle Scholar
[4] Mori, T., Representation of linearly additive random fields, Probab. Theory Related Fields, 92 (1992), 91–115.CrossRefGoogle Scholar
[5] Sato, Y., Distributions of stable random fields of Chentsov type, Nagoya Math. J., 123 (1991), 119–139.CrossRefGoogle Scholar
[6] Y, Sato. and Takenaka, S., On determinism of symmetric α-stable processes of generalized Chentsov type, Gaussian Random Fields, Series on Probab. and Statist. Vol. 1 (1991), World Scientific, 332–345.Google Scholar