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.
@article{1176995855,
author = {Junco, Andres Del},
title = {On the Decomposition of a Subadditive Stochastic Process},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 298-302},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995855}
}
Junco, Andres Del. On the Decomposition of a Subadditive Stochastic Process. Ann. Probab., Tome 5 (1977) no. 6, pp. 298-302. http://gdmltest.u-ga.fr/item/1176995855/