Skip to main content
SpringerLink
Log in

On weak convergence in \(\mathcal{M}\left({H}\right)\): relaxation of a sufficient condition

  • Published:
Sankhya A Aims and scope Submit manuscript

Abstract

Theorem 2.2 of Majumdar (Sankhyā 67:670–673, 2005) obtained two conditions that are necessary and jointly sufficient for weak convergence in \( {\mathcal{M}}\left({H}\right)\). In this note we significantly relax the second condition while maintaining the joint sufficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Billingsley, P. (1999). Convergence of probability measures. Wiley, NY.

    Book  MATH  Google Scholar 

  • Dudely, R.M. (1989). Real analysis and probability. Wadsworth and Brooks-Cole, CA.

    Google Scholar 

  • Majumdar, Suman (2005). On weak convergence in \({\mathcal{M}}\left({H}\right)\). Sankhyā, 67, Part 4, 670–673.

    MATH  Google Scholar 

  • Parthasarathy, K.R. (1967). Probability measures on metric spaces. Academic Press, NY.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, George Washington University, Washington, DC, 20052, USA

    Subrata Kundu

  2. Department of Statistics, University of Connecticut, 1 University Place, Stamford, CT, 06901, USA

    Suman Majumdar

  3. Department of Statistics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata, 700019, WB, India

    Arindam Sengupta

Authors
  1. Subrata Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suman Majumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arindam Sengupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arindam Sengupta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kundu, S., Majumdar, S. & Sengupta, A. On weak convergence in \(\mathcal{M}\left({H}\right)\): relaxation of a sufficient condition. Sankhya A 76, 146–149 (2014). https://doi.org/10.1007/s13171-013-0039-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13171-013-0039-7

Keywords and phrases

AMS (2000) subject classification.

Search

Navigation