Linear Isometric Non-Anticipative Transformations of Wiener Process

Zoran Ivković; Dražen Pantić

doi:10.1007/BF02731964

Chinese Annals of Mathematics, Series B ›› 2000, Vol. 21 ›› Issue (1) : 109 -114. DOI: 10.1007/BF02731964

Article

Linear Isometric Non-Anticipative Transformations of Wiener Process

Zoran Ivković ¹
, Dražen Pantić ¹

Author information +

History +

PDF

Abstract

The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.

Keywords

Resolution of identity / Separable Hilbert space / Wide sense Wiener process / Non-anticipative transformation / 60G12 / O211.6

Cite this article

Download citation ▾

Zoran Ivković, Dražen Pantić. Linear Isometric Non-Anticipative Transformations of Wiener Process. Chinese Annals of Mathematics, Series B, 2000, 21(1): 109-114 DOI:10.1007/BF02731964

登录浏览全文

4963

注册一个新账户忘记密码

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Cramér H. Stochastic processes as curves in Hilbert space. Theory Probability Appl, 1964, 9(2): 169-179

[2]	Hida T C. representations of Gaussian processes and their applications. Mem. College Sci. Univ. Kyoto., 1960, A33(1): 109-155

[3]	Stone M H. Linear transformations in Hilbert space and their applications to analysis, 1932, New York: Am. Math. Soc. Colloquium Publications, 25

[4]	Plessner A I, Rokhlin V A. Spectral theory of linear operators. Uspekhi Mat. Nauk., 1964, 1: 71-191

[5]	Lévy P. Sur une classé de courbes de léspace de Hilbert et sur une équation intégral non-linéaire. Ann. Sci. Ecole Normale Superieure, 1956, 73: 121-156