On the paper "weak convergence of some classes of martingales with jumps"

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1194-1200
Number of pages7
JournalAnnals of Probability
Volume35
Issue number3
DOIs
Publication statusPublished - 2007 May
Externally publishedYes

Fingerprint

Tightness
Weak Convergence
Martingale
Jump
Maximal Inequality
Entropy Condition
Random Measure
Empirical Process
Stochastic Integral
Parameter Space
Modulus
Entropy
Interval
Integer
Class
Weak convergence
Empirical process
Integral

Keywords

  • Entropy
  • Integer-valued random
  • Martingale
  • Maximal inequality
  • Measure
  • Weak convergence

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

On the paper "weak convergence of some classes of martingales with jumps". / Nishiyama, Yoichi.

In: Annals of Probability, Vol. 35, No. 3, 05.2007, p. 1194-1200.

Research output: Contribution to journalArticle

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