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
Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces
Download PDF
Download PDF
  • Article
  • Published: February 1999

Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces

  • Sandra Cerrai1 

Probability Theory and Related Fields volume 113, pages 85–114 (1999)Cite this article

  • 151 Accesses

  • 20 Citations

  • Metrics details

Abstract.

In the present paper we consider the transition semigroup P t related to some stochastic reaction-diffusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing effect in the Banach space of continuous functions , where ⊂ℝd is a bounded open set. In L 2() the only result proved is the strong Feller property, for d=1. Here we are able to prove that if f∈C ∞(ℝ) and d≤3, then for any and t>0. An important application is to the study of the ergodic properties of the system. These results are also of interest for some problem in stochastic control.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Università degli Studi di Firenze, Dimadefas, Via Lombroso 6/17, I-50134 Firenze, Italy. e-mail: cerrai@cibs.sns.it, , , , , , IT

    Sandra Cerrai

Authors
  1. Sandra Cerrai
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 20 August 1997 / Revised version: 27 May 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cerrai, S. Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces. Probab Theory Relat Fields 113, 85–114 (1999). https://doi.org/10.1007/s004400050203

Download citation

  • Issue Date: February 1999

  • DOI: https://doi.org/10.1007/s004400050203

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): 60J35
  • 60H15
  • 35K20
  • 60J25.
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