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
Relative entropy and mixing properties of infinite dimensional diffusions
Download PDF
Download PDF
  • Article
  • Published: March 1998

Relative entropy and mixing properties of infinite dimensional diffusions

  • A. F. Ramírez1 

Probability Theory and Related Fields volume 110, pages 369–395 (1998)Cite this article

  • 81 Accesses

  • 9 Citations

  • Metrics details

Summary.

Let η be a diffusion process taking values on the infinite dimensional space T Z, where T is the circle, and with components satisfying the equations dη i =σ i (η) dW i +b i (η) dt for some coefficients σ i and b i , i∈Z. Suppose we have an initial distribution μ and a sequence of times t n →∞ such that lim n →∞μS tn =ν exists, where S t is the semi-group of the process. We prove that if σ i and b i are bounded, of finite range, have uniformly bounded second order partial derivatives, and inf i ,ησ i (η)>0, then ν is invariant.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Centre de Mathématiques Appliquées, École Polytechnique, F-91128 Palaiseau Cedex, France, , , , , , FR

    A. F. Ramírez

Authors
  1. A. F. Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 12 September 1996 / In revised form: 10 November 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ramírez, A. Relative entropy and mixing properties of infinite dimensional diffusions. Probab Theory Relat Fields 110, 369–395 (1998). https://doi.org/10.1007/s004400050152

Download citation

  • Issue Date: March 1998

  • DOI: https://doi.org/10.1007/s004400050152

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): 60K35
  • 60J60
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