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Do minimal solutions of heat equations characterize diffusions?
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  • Published: September 1989

Do minimal solutions of heat equations characterize diffusions?

  • J. C. Taylor1 

Probability Theory and Related Fields volume 83, pages 321–330 (1989)Cite this article

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Summary

Brownian motion may be characterized as a process which, when composed with minimal parabolic functions, gives martingales. This note explores the extent to which this is true in general. For the diffusion associated with the Kohn Laplacian on the Heisenberg group it is shown to be false.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, McGill University, 805 Sherbrooke St. W., H3A 2K6, Montréal, Québec, Canada

    J. C. Taylor

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  1. J. C. Taylor
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Additional information

Materially supported by NSERC Operating Grant # A3108 and the IMA (U. of Minn.)

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Taylor, J.C. Do minimal solutions of heat equations characterize diffusions?. Probab. Th. Rel. Fields 83, 321–330 (1989). https://doi.org/10.1007/BF00964368

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  • Received: 12 December 1986

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF00964368

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Mathematical Biology
  • Heat Equation
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