Startseite Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms

  • Masayoshi Takeda EMAIL logo und Gerald Trutnau
Veröffentlicht/Copyright: 25. Februar 2012
Forum Mathematicum
Aus der Zeitschrift Band 24 Heft 2

Abstract.

Let Ed, d2, be an unbounded domain that is either open or closed. If it is closed, we assume that the boundary is locally the boundary of an extension domain. We present conservativeness criteria for (possibly reflected) diffusions with state space E and generator L which in the interior of E is given in the following suggestive form:

Lf=12i,j=1dj(aijif)+i=1dBiif.

Here the diffusion matrix (aij) is allowed to be non-symmetric, is merely assumed to consist of measurable functions, and satisfies locally a strict ellipticity condition. Moreover, B=(B1,...,Bd) is a divergence free vector field that satisfies some sector condition. Our main tool is a recently extended forward and backward martingale decomposition, which reduces to the well-known Lyons–Zheng decomposition in the symmetric case.

Keywords.: Diffusion processes; non-symmetric Dirichlet form; divergence form operators; conservativeness criteria; non-explosion test; Lyons–Zheng decomposition
Received: 2010-05-11
Revised: 2011-01-23
Published Online: 2012-02-25
Published in Print: 2012-March

© 2012 by Walter de Gruyter Berlin Boston

Artikel in diesem Heft

  1. Masthead
  2. Uniform weighted estimates for oscillatory singular integrals
  3. Solutions of the linear Boltzmann equation and some Dirichlet series
  4. Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
  5. Periodic flat resolutions and periodicity in group (co)homology
  6. Precompact noncompact reflexive Abelian groups
  7. Free profinite p-rings
  8. Cellular covers for R-modules and varieties of groups
  9. Time changes of local Dirichlet spaces by energy measures of harmonic functions
  10. A construction of a universal connection
  11. Finitely generated algebraic structures with various divisibility conditions
  12. Quasiprojective varieties admitting Zariski dense entire holomorphic curves
  13. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
https://doi.org/10.1515/form.2011.111
Schlagwörter für diesen Artikel
Diffusion processes; non-symmetric Dirichlet form; divergence form operators; conservativeness criteria; non-explosion test; Lyons–Zheng decomposition

Artikel in diesem Heft

  1. Masthead
  2. Uniform weighted estimates for oscillatory singular integrals
  3. Solutions of the linear Boltzmann equation and some Dirichlet series
  4. Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
  5. Periodic flat resolutions and periodicity in group (co)homology
  6. Precompact noncompact reflexive Abelian groups
  7. Free profinite p-rings
  8. Cellular covers for R-modules and varieties of groups
  9. Time changes of local Dirichlet spaces by energy measures of harmonic functions
  10. A construction of a universal connection
  11. Finitely generated algebraic structures with various divisibility conditions
  12. Quasiprojective varieties admitting Zariski dense entire holomorphic curves
  13. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 16.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/form.2011.111/html
Button zum nach oben scrollen