Properties of stochastic operators of order $\nu$ on a finite-dimensional simplex

Yu. Kh. Èshkabilov, J. Z. Istamov

Karshi State University, Karshi, 180119 Republic of Uzbekistan

Abstract: The necessary and sufficient conditions for stochasticity and bistochasticity of positive operators were analyzed. Key criteria for stochasticity of continuous positive operators in $\mathbb{R}^{m}$ were proved. The necessary and sufficient condition for these operators to be referred to as bistochastic was established.

Keywords: stochastic operator, bistochastic operator, cone, positive operator, rearrangements of cone element.

UDC: 517.98

Received: 28.05.2024
Accepted: 04.09.2024

DOI: 10.26907/2541-7746.2024.4.651-659