Open Access
May 2007 On the paper “Weak convergence of some classes of martingales with jumps”
Yoichi Nishiyama
Ann. Probab. 35(3): 1194-1200 (May 2007). DOI: 10.1214/009117906000000755


This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685–712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniques developed in the modern theory of empirical processes.


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Yoichi Nishiyama. "On the paper “Weak convergence of some classes of martingales with jumps”." Ann. Probab. 35 (3) 1194 - 1200, May 2007.


Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1130.60028
MathSciNet: MR2319720
Digital Object Identifier: 10.1214/009117906000000755

Primary: 60F05 , 60F17

Keywords: Entropy , integer-valued random measure , martingale , maximal inequality , weak convergence

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • May 2007
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