Uniformly distributed hitting position for two-dimensional anisotropic diffusion process: the limit normed curve

Let $W_1$ and $W_2$ be independent Wiener processes on the halfline, and let $W^{(a)}=(W_1,aW_2)$ ($a\ge1$). We consider open neighborhoods of the initial point with the uniform hitting density. This property determines uniquely the form of neighborhood. The main result: there exists a limit form of such a neighborhood as $a\to\infty$. Properties of such a limit form are under investigation. Bibl. 2 titles.