Published: 1951 Received: -Available on J-STAGE: August 29, 2006Accepted: -
Advance online publication: -
Revised: -
Correction information
Date of correction: August 29, 2006Reason for correction: -Correction: AUTHORDetails: Wrong : Kiyosi ITO1) Right : Kiyosi ITÔ1)
Date of correction: August 29, 2006Reason for correction: -Correction: CITATIONDetails: Right : 1) N. Wiener: The homogeneous chaos, Amer. Journ. Math. Vol. LV, No. 4, 1938. 2) S. Kakntani: Determination of the spectrum of the flow of Brownian motion, Proc. Nat. Acad. Sci., U. S. A. 36 (1950), 319-323. 3) K. Itô Stochastic integral, Proc. Imp. Acad. Tokyo, Vol. XX, No. 8 1944. 4) A. Kolmogoroff: Grundbegriffe der Wahrscheinlichkeilsrechnung, Berlin, 1933. The consistency-condition is well satisfied by virtue of the property of multivariate Gaussian distribution. 5) P. Lévy: Thérie de l'addition des variariables aléatoires, Paris, 1937. 6) An elementary function of (t1,…,tp) is defined as a linear combination of the characteristic functions of the sets of the form E1×…×Ep, Ei eΒ, i=1 2,…,n. 7) (j)-(i) means that (j)≡(j1,…jq) is a permutation of (i)≡(i1,…,ip). 8) R. H. Cameron and W. T. Martin: The orthogonal development of non-linear functionals in series of Fourier-Hermite functions. 9) loc. cit. 2).
Date of correction: August 29, 2006Reason for correction: -Correction: PDF FILEDetails: -