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