We give an elementary proof of the decomposition of a subadditive stochastic process as an additive process plus a positive subadditive process with time constant 0. The proof is based on two ideas. The first is a general idea for obtaining a kind of weak limit point for $L_1$-bounded sequences of random variables, based on the martingale convergence theorem. The second is a general result about martingales which seems to be new and is of independent interest.
"On the Decomposition of a Subadditive Stochastic Process." Ann. Probab. 5 (2) 298 - 302, April, 1977. https://doi.org/10.1214/aop/1176995855