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Uniqueness for isotropic diffusions with a linear drift
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  • Published: 02 January 2004

Uniqueness for isotropic diffusions with a linear drift

  • Jan M. Swart1 

Probability Theory and Related Fields volume 128, pages 517–524 (2004)Cite this article

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Abstract.

This paper proves that-valued solutions to the SDE are unique in distribution, when D⊂ d is convex and open, θ∈D, c>0, is positive and locally Lipschitz on D and zero on ∂D, and {x∈D:g(x)≥r} is convex for r sufficiently small. The proof (for θ=0) is based on the transformation X t ↦e ct X t , which removes the drift, and a random time change. Although the set-up is rather specialized the result gives uniqueness for some SDE’s that cannot be treated by any of the conventional techniques.

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Authors and Affiliations

  1. University Erlangen-Nuremberg, Bismarckstraße 1½, 91054, Erlangen, Germany

    Jan M. Swart

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  1. Jan M. Swart
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Correspondence to Jan M. Swart.

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Mathematics Subject Classification (2000): 60J60, 60H10

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Swart, J. Uniqueness for isotropic diffusions with a linear drift. Probab. Theory Relat. Fields 128, 517–524 (2004). https://doi.org/10.1007/s00440-003-0315-x

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  • Received: 26 January 2003

  • Revised: 03 September 2003

  • Published: 02 January 2004

  • Issue Date: April 2004

  • DOI: https://doi.org/10.1007/s00440-003-0315-x

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Keywords

  •  Diffusion process
  • Stochastic differential equation
  • Weak uniqueness
  • Distribution uniqueness
  • Isotropic diffusion
  • Random time change
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