Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D

Abstract

Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation, we solve the combinatorial problems and reduce these equations to a set of linear equations for a finite number of unknown functions. Imposing natural conditions, we obtain a closed system of linear equations which can be solved for a given surface. Its solutions can be used to calculate the distribution of hitting probabilities for a regular surface with compact support. In order to verify the accuracy of the approximate distribution of hitting probabilities, numerical analysis is being made for a chosen surface.