Vol. 42, No. 2, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
A decomposition theorem for biadditive processes

W. N. Hudson

Vol. 42 (1972), No. 2, 333–341
Abstract

This paper treats a class of stochastic processes called biadditive processes and gives a proof of a decomposition of their sample functions. Informally, a biadditive proces X(s,t) is a process indexed by two time parameters whose “increments ” over disjoint rectangles are independent. The increments of such a process are the second differences

X (s2,t2)− X (s1,t2)− X (s2,t1) +X (s1,t1)

where s1 < s2 and t1 < t2. The decomposition theorem states that every centered biadditive process is the sum of four independent biadditive processes: one with jumps in both variables, two with jumps in one variable and continuous in probability in the other, and a fourth process which is jointly continuous in probability.

Mathematical Subject Classification
Primary: 60J30
Milestones
Received: 10 March 1972
Published: 1 August 1972
Authors
W. N. Hudson