On the paper ``Weak convergence of some classes of martingales with jumps''

Details On the paper ``Weak convergence of some classes of martingales with jumps'' On the paper ``Weak convergence of some classes of martingales with jumps''

2007-07-31

arxiv.org/abs/0707.4536v1

Annals of Probability 2007, Vol. 35, No. 3, 1194-1200

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000755 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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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