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Abstract <p>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.</p>

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Mean Value of the Part of the Perimeter of a Convex Hull Generated by a Poisson Point Process

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • I. M. Khamdamov,
  • Kh. M. Mamatov,
  • Z. S. Chay,
  • E. R. Tadjikhodjayeva

摘要

Abstract

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.