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

  • Masayoshi Takeda EMAIL logo and Gerald Trutnau
Published/Copyright: February 25, 2012
Forum Mathematicum
From the journal Volume 24 Issue 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

Articles in the same Issue

  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
Keywords for this article
Diffusion processes; non-symmetric Dirichlet form; divergence form operators; conservativeness criteria; non-explosion test; Lyons–Zheng decomposition

Articles in the same Issue

  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
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