Goursat Problem over Unit Cube in First Quadrant of R~n (with applications to existence of copulas)

摘要

In the present paper we consider the Goursat problem, which appears to be closely related to construction of the so called copulas. Unlike the classical approach applied by Vladimirov [7] where he solves the two-variable problem we investigate the n-dimensional case. In addition to that we also prove that there exists a unique solution to the Goursat problem.