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On the Uniform Continuity of Wiener Process with a Multidimensional Parameter

Published online by Cambridge University Press:  22 January 2016

Takeyuki Hida
Takeyuki Hida*
Affiliation:
Mathematical Institute, Aichi-Gakugei University
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Let X(A, ω), ω∈Ω, be Wiener process on the probability space (Ω, B, P) depending on a point A of an N dimensional Euclidean space EN.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 13 , June 1958 , pp. 53 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1958

References

[1] Lévy, P., Processus stochastiques et mouvement brownien, Gauthier-Villars, Paris (1948).Google Scholar
[2] Sirao, T., On the uniform continuity of Wiener process, J. Math. Soc. Japan, vol. 6 (1954), pp. 332–335.Google Scholar
[3] Chung, K. L. and Erdös, P., On the application of the Borel Cantelli lemma, Trans. Amer. Math. Soc., vol. 72 (1952), pp. 179–189.Google Scholar