Abstract.
Let ℒ≔Δ/2+(∇φ/φ) ·∇ be a generalized Schrödinger operator or generator of Nelsons diffusion, defined on C ∞ 0(D) where φ is a continuous and strictly positive function on an open domain D⊂ℝd such that ∇φ∈L loc 2(D). Some results are given about the two questions below: (i) Whether does ℒ generate a unique semigroup in L 1(D, φ2 dx)? (ii) Whether the semigroup determined by ℒ is strong Feller?
Author information
Authors and Affiliations
Additional information
Received: 21 October 1997 / Revised version: 3 September 1998
Rights and permissions
About this article
Cite this article
Liming, W. Uniqueness of Nelsons diffusions. Probab. Theory Relat. Fields 114, 549–585 (1999). https://doi.org/10.1007/s004400050234
Published:
Issue Date:
DOI: https://doi.org/10.1007/s004400050234
- Mathematics Subject Classification (1991): 60J60, 60H10, 31C25, 81Q10