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Laws of large numbers for semimartingales with applications to stochastic regression
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  • Published: June 1989

Laws of large numbers for semimartingales with applications to stochastic regression

  • A. Le Breton1 &
  • M. Musiela2 

Probability Theory and Related Fields volume 81, pages 275–290 (1989)Cite this article

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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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Author information

Authors and Affiliations

  1. Laboratoire IMAG-TIM 3, University of Grenoble, BP 68, F-38402, Saint-Martin d'Heres Cedex, France

    A. Le Breton

  2. Department of Statistics, University of New South Wales, P.O. Box 1, Kensington, New South Wales, Australia

    M. Musiela

Authors
  1. A. Le Breton
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  2. M. Musiela
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Additional information

Research supported by the Australian Research Grants Scheme

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Cite this article

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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  • Received: 17 June 1987

  • Revised: 30 August 1988

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00319555

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Keywords

  • Linear Regression
  • Regression Model
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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