A decomposition theorem for biadditive processes

W. N. Hudson

Vol. 42 (1972), No. 2, 333–341

DOI: 10.2140/pjm.1972.42.333

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

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