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
Degenerate stochastic differential equations and super-Markov chains
Download PDF
Download PDF
  • Published: August 2002

Degenerate stochastic differential equations and super-Markov chains

  • S. R. Athreya1,
  • M. T. Barlow2,
  • R. F. Bass3 &
  • …
  • E. A. Perkins2 

Probability Theory and Related Fields volume 123, pages 484–520 (2002)Cite this article

  • 210 Accesses

  • 38 Citations

  • Metrics details

Abstract.

 We consider diffusions corresponding to the generator

for continuous with γ i nonnegative. We show uniqueness for the corresponding martingale problem under certain non-degeneracy conditions on b i , γ i and present a counter-example when these conditions are not satisfied. As a special case, we establish uniqueness in law for some classes of super-Markov chains with state dependent branching rates and spatial motions.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Stat-Math Unit, Indian Statistical Institute, New Delhi, India – 110016, , , , , , IN

    S. R. Athreya

  2. Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2, , , , , , CA

    M. T. Barlow & E. A. Perkins

  3. Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA, , , , , , US

    R. F. Bass

Authors
  1. S. R. Athreya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. T. Barlow
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. F. Bass
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. A. Perkins
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 31 March 2001 / Revised version: 6 November 2001 / Published online: 1 July 2002

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Athreya, S., Barlow, M., Bass, R. et al. Degenerate stochastic differential equations and super-Markov chains. Probab Theory Relat Fields 123, 484–520 (2002). https://doi.org/10.1007/s004400100191

Download citation

  • Issue Date: August 2002

  • DOI: https://doi.org/10.1007/s004400100191

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

Keywords

  • Differential Equation
  • Stochastic Differential Equation
  • Spatial Motion
  • Martingale Problem
  • Degenerate Stochastic Differential Equation
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