A uniformly distributed hitting position for a two-dimensional anisotropic diffusion process: The limit normed curve

Let W₁ and W₂ be two independent Wiener processes on a half-line, and let W^(a)=(W₁, aW₂) (a≥1). We consider open neighborhoods of the initial point with uniform hitting distribution. This property uniquely determines the form of a neighborhood. The main result is as follows: such a neighborhood has a limit form as a→∞. Properties of the limit form are studied. Bibliography: 2 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 333–348.