Laws of large numbers for semimartingales with applications to stochastic regression
type: Item
instance of: scholarly article
title: Laws of large numbers for semimartingales with applications to stochastic regression
zbMATH Open document ID: 0662.60043
DOI: 10.1007/BF00319555
author: Alain Le Breton
author: M. Musiela
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 4082621
zbMATH Keywords: Strong laws of large numbers
zbMATH Keywords: local martingales
zbMATH Keywords: local submartingales
zbMATH Keywords: Borel-Cantelli-type lemma for local martingales of finite variation
zbMATH Keywords: strong consistency of estimates
zbMATH Keywords: linear regression models
MaRDI profile type: Publication
cites work: Strong consistency of least squares estimates in dynamic models
cites work: A form of the Borel-Cantelli lemma
cites work: A short note on the conditional Borel-Cantelli lemma
cites work: Quasi-least-squares estimation in semimartingale regression models
cites work: Strong consistency of least squares estimators in linear regression models
cites work: Local Convergence of Martingales and the Law of Large Numbers
cites work: A law of large numbers for identically distributed martingale differences
cites work: Another note on the Borel-Cantelli lemma and the strong law, with the Poisson approximation as a by-product
cites work: Conditional generalizations of strong laws which conclude the partial sums converge almost surely
cites work: A stronger form of the Borel-Cantelli lemma
cites work: Calcul stochastique et problèmes de martingales
cites work: Q4187080
cites work: On the existence and path properties of stochastic integrals
cites work: On the strong law of large numbers for multivariate martingales
cites work: Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems
cites work: Q3744975
cites work: Convergence comparée des processus
cites work: A strong law of large numbers for local martingales
cites work: Q3742434
cites work: Q5644823
cites work: On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals
cites work: Q3736759
cites work: Q4084474
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4082621