Laws of large numbers for semimartingales with applications to stochastic regression
Strong laws of large numbers for matrix-normalized vector-valued local martingales are established. The results are derived from strong laws for positive local submartingales and purely discontinuous local martingales and a Borel-Cantelli-type lemma for local martingales of finite variation. The multivariate strong laws are applied to study strong consistency of estimates in stochastic linear regression models.
Borel-Cantelli-type lemma for local martingales of finite variation
scientific article; zbMATH DE number 4082621
scientific article