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Uniqueness of Nelsons diffusions
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  • Published: 01 July 1999

Uniqueness of Nelsons diffusions

  • Wu Liming1 

Probability Theory and Related Fields volume 114, pages 549–585 (1999)Cite this article

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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?

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, Université Blaise Pascal, F-63177 Aubiere, France. e-mail: wuliming@ucfma.univ-bpclermont.fr , France

    Wu Liming

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  1. Wu Liming
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Received: 21 October 1997 / Revised version: 3 September 1998

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Liming, W. Uniqueness of Nelsons diffusions. Probab. Theory Relat. Fields 114, 549–585 (1999). https://doi.org/10.1007/s004400050234

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  • Published: 01 July 1999

  • Issue Date: July 1999

  • DOI: https://doi.org/10.1007/s004400050234

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  • Mathematics Subject Classification (1991): 60J60, 60H10, 31C25, 81Q10
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