Boundary behaviour of conditional diffusion processes

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.