Geodesic
Diffusion Processes and Elliptic Differential Equations Degenerating at the Boundary of the Domain
Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 430-451

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In this paper Markov diffusion processes with continuous paths are studied. We give the definitions of attracting, repelling, unattainable and regular boundaries. Effective sufficient conditions for each type expressed in terms of the coefficients of the equation (2) are given also. These conditions are also necessary for additional assumptions. 
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     author = {R. Z. Khas'minskii},
     title = {Diffusion {Processes} and {Elliptic} {Differential} {Equations} {Degenerating} at the {Boundary} of the {Domain}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {430--451},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1958},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a4/}
}
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R. Z. Khas'minskii. Diffusion Processes and Elliptic Differential Equations Degenerating at the Boundary of the Domain. Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 430-451. http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a4/