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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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Weak Convergence to Stochastic Integrals

Weak Convergence to Stochastic Integrals

Chapter:
(p.496) 30 Weak Convergence to Stochastic Integrals
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0030

The main object of this final chapter is to prove an essential companion result to the FCLT, the convergence of certain normalized random sums to stochastic integrals with respect to Brownian motion. Some preliminary theory is given relating to random functionals on C and processes in continuous time.

Keywords:   diffusion process, filtration, Itô's rule, martingale, progressive measurability, random functional, stochastic integral

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