Vol. 36, No. 2, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Volterra transformations of the Wiener measure on the space of continuous functions of two variables

W. N. Hudson

Vol. 36 (1971), No. 2, 335–349
Abstract

The transformation of Wiener integrals over the space C2 of continuous functions of two variables by a Volterra operator T is investigated. The operator T is defined for functions x C2 by

                 ∫  ∫
s  t
T x(s,t) = x(s,t)+ 0  0 K(u,v)x(u,v)dudv,

where the kernel K(u,v) is continuous. A stochastic integral analogous to K. Ito’s is defined and used to determine a Jacobian J(x) for T such that if F(x) is a Wiener measurable functional, Γ a Wiener measurable set, and m Wiener measure,

∫           ∫
F(x)dm =       F (Tx)J(x)dm.
Γ          τ−1(Γ )

Mathematical Subject Classification
Primary: 28.46
Secondary: 60.00
Milestones
Received: 21 April 1970
Published: 1 February 1971
Authors
W. N. Hudson