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Mean value of the part of the perimeter of a convex hull generated by a Poisson point process
https://doi.org/10.26907/0021-3446-2025-11-89-96
Abstract
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.
About the Authors
I. M. Khamdamov
University of Public Safety of the Republic of Uzbekistan
Uzbekistan
Uzbekistan
Isakjan M. Khamdamov
Zangiatinsky dist., Chorsy village, Tashkent, 100109
Kh. M. Mamatov
University of Public Safety of the Republic of Uzbekistan
Uzbekistan
Uzbekistan
Khusniddin M. Mamatov
Zangiatinsky dist., Chorsy village, Tashkent, 100109
Z. S. Chay
Tashkent University of Information Technologies;
Tashkent International University of Education
Uzbekistan
Uzbekistan
Zoya S. Chay
108 Amir Temur Ave., Tashkent, 100089,
Yashnabad dist., Tuzel-2 massif, Imam Bukhari str., Tashkent, 100207
E. R. Tadjikhodjayeva
Tashkent International University of Education
Uzbekistan
Uzbekistan
Elvira R. Tadjikhodjayeva
Yashnabad dist., Tuzel-2 massif, Imam Bukhari str., Tashkent, 100207
References
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Review
For citations:
Khamdamov I.M., Mamatov Kh.M., Chay Z.S., Tadjikhodjayeva E.R. Mean value of the part of the perimeter of a convex hull generated by a Poisson point process. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(11):89-96. (In Russ.) https://doi.org/10.26907/0021-3446-2025-11-89-96
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