Skip to main content
SpringerLink
Log in

The α-orthogonal complements of regular Dirichlet subspaces for one-dimensional Brownian motion

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

Roughly speaking a regular Dirichlet subspace of a Dirichlet form is a subspace which is also a regular Dirichlet form on the same state space. In particular, the domain of regular Dirichlet subspace is a closed subspace of the Hilbert space induced by the domain and α-inner product of original Dirichlet form. We investigate the orthogonal complement of regular Dirichlet subspace for one-dimensional Brownian motion in this paper. Our main results indicate that this orthogonal complement has a very close connection with the α-harmonic equation under Neumann type condition.

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

  1. Adams R A, Fournier J J F. Sobolev Spaces, 2nd ed. Amsterdam: Elsevier/Academic Press, 2003

    MATH  Google Scholar 

  2. Chen Z-Q, Fukushima M. Symmetric Markov Processes, Time Change, and Boundary Theory. Princeton: Princeton University Press, 2012

    MATH  Google Scholar 

  3. Fang X, Fukushima M, Ying J. On regular Dirichlet subspaces of H1(I) and associated linear diffusions. Osaka J Math, 2005, 42: 27–41

    MathSciNet  MATH  Google Scholar 

  4. Fang X, He P, Ying J. Dirichlet forms associated with linear diffusions. Chin Ann Math Ser B, 2010, 31: 507–518

    Article  MathSciNet  MATH  Google Scholar 

  5. Fukushima M, Oshima Y, Takeda M. Dirichlet Forms and Symmetric Markov Processes, 2nd ed. Berlin: Walter de Gruyter, 2011

    MATH  Google Scholar 

  6. Ito K, McKean H. Diffusion Processes and Their Sample Paths. Berlin-New York: Springer-Verlag, 1974

    MATH  Google Scholar 

  7. Li L, Ying J. On structure of regular subspaces of one-dimensional Brownian motion. ArXiv:1412.1896, 2014

  8. Li L, Ying J. Regular subspaces of Dirichlet forms. In: Festschrift Masatoshi Fukushima. In Honor of Masatoshi Fukushima’s Sanju. Singapore: World Scientific, 2015, 397–420

    Chapter  Google Scholar 

  9. Rogers L C G, Williams D. Diffusions, Markov Processes, and Martingales. Cambridge: Cambridge University Press, 2000

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    LiPing Li & XiuCui Song

Authors
  1. LiPing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. XiuCui Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to LiPing Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, L., Song, X. The α-orthogonal complements of regular Dirichlet subspaces for one-dimensional Brownian motion. Sci. China Math. 59, 2019–2026 (2016). https://doi.org/10.1007/s11425-014-0869-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-014-0869-1

Keywords

MSC(2010)

Search

Navigation