Mean Value of the Part of the Perimeter of a Convex Hull Generated by a Poisson Point Process
I. M. KhamdamovUniversity of Public Safety of the Republic of Uzbekistan, 100109, Tashkent, Republic of UzbekistanKh. M. MamatovUniversity of Public Safety of the Republic of Uzbekistan, 100109, Tashkent, Republic of UzbekistanZ. S. ChayTashkent University of Information Technologies, 100089, Tashkent, Republic of UzbekistanE. R. TadjikhodjayevaTashkent International University of Education, 100207, Tashkent, Republic of Uzbekistan
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Vertex processes of the convex hull generated by inhomogeneous Poisson point processes within a parabola in the plane are studied. Distribution laws and the conditional distribution of vertex processes are used to construct a stationary Markov process to find an exact expression for the expectation of the part of the perimeter between the initial vertices of the convex hull.
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