Summary
Strong laws of large numbers for matrix-normalised 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.
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Research supported by the Australian Research Grants Scheme
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Le Breton, A., Musiela, M. Laws of large numbers for semimartingales with applications to stochastic regression. Probab. Th. Rel. Fields 81, 275–290 (1989). https://doi.org/10.1007/BF00319555
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DOI: https://doi.org/10.1007/BF00319555