Geodesic
Boundary behaviour of conditional diffusion processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 160-163 
Yu. I. Kifer. Boundary behaviour of conditional diffusion processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 160-163. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a12/
@article{TVP_1973_18_1_a12,
     author = {Yu. I. Kifer},
     title = {Boundary behaviour of conditional diffusion processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {160--163},
     year = {1973},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a bounded domain in $R^n$ of class $A^{(2)}$ with the boundary $\Gamma$, and $x_t$ be a diffusion process in $G$ with absorption on $\Gamma$. Denote by $q(x,\gamma)$ the distribution density of the exit point of $x_t$ on $\Gamma$, and let $\widehat x_t$ be the conditional process given that $x_t$ is absorbed at a point $o$. In the paper, the behaviour of the function $q(x,o)$ as $x\to o$ and of the process $\widehat x_t$ near $o$ is studied.