Mean value of the part of the perimeter of a convex hull generated by a Poisson point process

This paper investigates vertex processes of the convex hull generated by inhomogeneous Poisson point processes within a parabola in the plane. Using distribution laws and the conditional distribution of the vertex processes, a stationary Markov process is constructed to find an exact expression for the mathematical expectation of the part of the perimeter between the initial vertices of the convex hull.