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Ito’s formula and Levy’s Laplacian

Published online by Cambridge University Press:  22 January 2016

Kimiaki Saito
Kimiaki Saito*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464, Japan
*
Department of Mathematics Meijo University, Tenpaku-ku, Nagoya 468, Japan
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The class of normal functionals

is, as is well known, adapted to the domain of Lévy’s Laplacian and plays important roles in the works by P. Lévy and T. Hida (cf. [1], [2] and [8]), where Bx denotes one-dimensional parameter white noise and denotes the renormalization of

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 108 , December 1987 , pp. 67 - 76
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Hida, T., Brownian motion in Applications of Mathematics 11, Springer-Verlag (1980).Google Scholar
[ 2 ] Hida, T., Brownian motion and its functionals, Ricerche di Matematica, Vol. XXXIV, fase, I° (1985).Google Scholar
[ 3 ] Hille, E. and Phillips, R. S., Functional Analysis and Semi-groups, Colloq. Publ. Amer. Math. Soc., (1957).Google Scholar
[ 4 ] Itô, K., Foundations of stochastic differential equations in infinite dimensional spaces, CBMS-NSF Regional Conference Series in Applied Math., 47 (1984).Google Scholar
[ 5 ] Kubo, I., Ito formula for generalized Brownian functionals, Lecture Notes in Control and Information Science, 49 (1983), 156–166.Google Scholar
[ 6 ] Kubo, I. and Takenaka, S., Calculus on Gaussian white noise, I-IV Proc. Japan Acad., 56A (1980), 376–380, 411–416, 57A (1981), 433–437, 58A (1982), 186–189.Google Scholar
[ 7 ] Kuo, H.-H., On Laplacian operators of generalized Brownian functionals, Lecture Notes in Mathematics, 1203, Springer-Verlag (1986), 119–128.Google Scholar
[ 8 ] Levy, P., Problèmes concret d’analyse fonctionnelle, Gauthier-Villars (1951).Google Scholar