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.
