Geodesic
The Local Diffusions of a Harmonic Sheaf
Canadian mathematical bulletin, Tome 8 (1965) no. 3, pp. 307-316

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It is well known that the Laplacian operator is the infinitesimal generator of Brownian motion in Rn. Moreover, the classical harmonic measures are the hitting measures of Brownian motion. In other words, there is a natural correspondence between the Brownian motion and the classical harmonic functions. In this paper we will show that any family of abstract harmonic functions satisfying the axioms of M. Brelot [4] are annihilated by the infinitesimal generator of a diffusion, and that the corresponding harmonic measures are the hitting measures of the diffusion. This answers a question raised by P. A. Meyer [11] who has proved the existence of a Markov semi-group associated with a harmonic sheaf. 
Dawson, Donald A. The Local Diffusions of a Harmonic Sheaf. Canadian mathematical bulletin, Tome 8 (1965) no. 3, pp. 307-316. doi: 10.4153/CMB-1965-021-4
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     title = {The {Local} {Diffusions} of a {Harmonic} {Sheaf}},
     journal = {Canadian mathematical bulletin},
     pages = {307--316},
     year = {1965},
     volume = {8},
     number = {3},
     doi = {10.4153/CMB-1965-021-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-021-4/}
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