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
Potential theory of subordinate killed Brownian motion in a domain
Download PDF
Download PDF
  • Published: April 2003

Potential theory of subordinate killed Brownian motion in a domain

  • Renming Song1 &
  • Zoran Vondraček2 

Probability Theory and Related Fields volume 125, pages 578–592 (2003)Cite this article

  • 456 Accesses

  • 77 Citations

  • Metrics details

Abstract.

 Subordination of a killed Brownian motion in a bounded domain D⊂ℝd via an α/2-stable subordinator gives a process Z t whose infinitesimal generator is −(−Δ| D )α/2, the fractional power of the negative Dirichlet Laplacian. In this paper we study the properties of the process Z t in a Lipschitz domain D by comparing the process with the rotationally invariant α-stable process killed upon exiting D. We show that these processes have comparable killing measures, prove the intrinsic ultracontractivity of the generator of Z t , prove the intrinsic ultracontractivity of the semigroup of Z t , and, in the case when D is a bounded C 1,1 domain, obtain bounds on the Green function and the jumping kernel of Z t .

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL 61801, USA. e-mail: rsong@math.uiuc.edu, , , , , , US

    Renming Song

  2. Department of Mathematics, University of Zagreb, Zagreb, Croatia. e-mail: vondra@math.hr, , , , , , HR

    Zoran Vondraček

Authors
  1. Renming Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zoran Vondraček
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 4 April 2002 / Revised version: 1 July 2002 / Published online: 19 December 2002

This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut Oberwolfach. We thank the Institute for the hospitality.

The research of the first author is supported in part by NSF Grant DMS-9803240.

The research of the second author is supported in part by MZT grant 037008 of the Republic of Croatia.

Mathematics Subject Classification (2000): Primary 60J45; Secondary 60J75, 31C25

Key words or phrases: Killed Brownian motions – Stable processes – Subordination – Fractional Laplacian

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Song, R., Vondraček, Z. Potential theory of subordinate killed Brownian motion in a domain. Probab. Theory Relat. Fields 125, 578–592 (2003). https://doi.org/10.1007/s00440-002-0251-1

Download citation

  • Issue Date: April 2003

  • DOI: https://doi.org/10.1007/s00440-002-0251-1

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

  • Brownian Motion
  • Bounded Domain
  • Green Function
  • Potential Theory
  • Lipschitz Domain
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