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April 2000 Weak convergence of some classes of martingales with jumps
Yoichi Nishiyama
Ann. Probab. 28(2): 685-712 (April 2000). DOI: 10.1214/aop/1019160257

Abstract

This paper deals with weak convergence of stochastic integrals with respect to multivariate point processes. The results are given in terms of an entropy condition for partitioning of the index set of the integrands, which is a sort of $L^2$-bracketing.We also consider $\ell^\infty$-valued martingale difference arrays, and present natural generalizations of Jain–Marcus’s and Ossiander’s central limit theorems. As an application,the asymptotic behavior of log-likelihood ratio random fields in general statistical experiments with abstract parameters is derived.

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Yoichi Nishiyama. "Weak convergence of some classes of martingales with jumps." Ann. Probab. 28 (2) 685 - 712, April 2000. https://doi.org/10.1214/aop/1019160257

Information

Published: April 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1128.60305
MathSciNet: MR1782271
Digital Object Identifier: 10.1214/aop/1019160257

Subjects:
Primary: 60F05, 60F17, 62F20

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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