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A Note on Lévy’s Brownian motion

Published online by Cambridge University Press:  22 January 2016

Si Si
Si Si*
Affiliation:
Department of Mathematics Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan, and Department of Mathematics, Rangoon University, Rangoon, Burma
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The Lévy Brownian motion with multidimensional parameter was introduced and discussed in his book [1] and it is known as the most important random field. Many approaches have been made to the investigation of the Lévy Brownian motion by H.P. McKean [7], Yu. A. Rozanov and others, by using various techniques.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 108 , December 1987 , pp. 121 - 130
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Lévy, P., Processus stochastiques et Mouvment Brownein, Gautier Villars, Paris, (1948).Google Scholar
[ 2 ] Lévy, P., Random functions: General theory with special reference to Laplacian random functions, Univ. of California Publications in Statistics, 1 (1953), 331–390.Google Scholar
[ 3 ] Lévy, P., A special problem of Brownian motion, and a general theory of Gaussian Random functions, Proceeding of the Third Berkeley Symposium on Math. Stat. and Prob., 2 (1956), 133–175.Google Scholar
[ 4 ] Lévy, P., Random functions: A Laplacian random function depending on a point of Hilbert space, Univ. of California Publications in Statistics, 2, No. 10 (1956), 195–206.Google Scholar
[ 5 ] Hida, T., Canonical representation of Gaussian processes and their applications, Mem. Coll. Sci. Univ. Kyoto, 33 (1960), 258–351.Google Scholar
[ 6 ] Hida, T. and Hitsuda, M., Gaussian Processes, Kinokuniya Pub. Co. 1976 (in Japanese).Google Scholar
[ 7 ] McKean, H. P. Jr., Brownian motion with a several-dimensional time, Theory Probab. Appl., 8 (1963), 335–354.CrossRefGoogle Scholar