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Le Breton, Alain; Musiela, Marek

Laws of large numbers for semimartingales with applications to stochastic regression. (English) Zbl 0662.60043

Probab. Theory Relat. Fields 81, No. 2, 275-290 (1989).
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.
Reviewer: A.Le Breton

Cited in 3 Documents

MSC:

60F15 Strong limit theorems
62J05 Linear regression; mixed models
60G42 Martingales with discrete parameter

Keywords:

Strong laws of large numbers; local martingales; local submartingales; Borel-Cantelli-type lemma for local martingales of finite variation; strong consistency of estimates; linear regression models
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References:

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