Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Some central limit theorems for ℓ∞-valued semimartingales and their applications
Download PDF
Download PDF
  • Published: August 1997

Some central limit theorems for ℓ∞-valued semimartingales and their applications

  • Yoichi Nishiyama1 

Probability Theory and Related Fields volume 108, pages 459–494 (1997)Cite this article

  • 178 Accesses

  • 15 Citations

  • Metrics details

Summary.

This paper is devoted to the generalization of central limit theorems for empirical processes to several types of ℓ∞(Ψ)-valued continuous-time stochastic processes t⇝X t n=(X t n ,ψ|ψ∈Ψ), where Ψ is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t⇝X t n ,ψ is: (i) a general semimartingale; (ii) a stochastic integral of a predictable function with respect to an integer-valued random measure; (iii) a continuous local martingale. Some applications to statistical inference problems are also presented. We prove the functional asymptotic normality of generalized Nelson-Aalen's estimator in the multiplicative intensity model for marked point processes. Its asymptotic efficiency in the sense of convolution theorem is also shown. The asymptotic behavior of log-likelihood ratio random fields of certain continuous semimartingales is derived.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan (e-mail: nisiyama@ism.ac.jp), , , , , , JP

    Yoichi Nishiyama

Authors
  1. Yoichi Nishiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 6 May 1996 / In revised form: 4 February 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nishiyama, Y. Some central limit theorems for ℓ∞-valued semimartingales and their applications. Probab Theory Relat Fields 108, 459–494 (1997). https://doi.org/10.1007/s004400050117

Download citation

  • Issue Date: August 1997

  • DOI: https://doi.org/10.1007/s004400050117

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (1991): 60F05
  • 60F17
  • 62E20
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature