A Family of Volterra Cubic Stochastic Operators

Uygun Jamilov; Andrejs Reinfelds

A Family of Volterra Cubic Stochastic Operators

Uygun Jamilov
, Andrejs Reinfelds

Department of Mathematics

Academy of Sciences of the Republic of Uzbekistan

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We consider a convex combination of Volterra cubic stochastic operators defined on a two-dimensional simplex depending on the parameter θ and study their trajectory behaviours. We show that at the values θ = 1/2, the trajectories change their orientation. Moreover, for θ < 1/2 any Volterra cubic stochastic operator has the property being regular and it is non-ergodic while θ > 1/2.

Original language	English
Pages (from-to)	19-30
Number of pages	12
Journal	Journal of Convex Analysis
Volume	28
Issue number	1
Publication status	Published - 2021

Keywords

Cubic stochastic operator
Quadratic stochastic operator
Volterra operator

OECD Field of Science

1.1 Mathematics

Cite this

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title = "A Family of Volterra Cubic Stochastic Operators",

abstract = "We consider a convex combination of Volterra cubic stochastic operators defined on a two-dimensional simplex depending on the parameter θ and study their trajectory behaviours. We show that at the values θ = 1/2, the trajectories change their orientation. Moreover, for θ < 1/2 any Volterra cubic stochastic operator has the property being regular and it is non-ergodic while θ > 1/2.",

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T1 - A Family of Volterra Cubic Stochastic Operators

AU - Jamilov, Uygun

AU - Reinfelds, Andrejs

N1 - Publisher Copyright: © Heldermann Verlag

PY - 2021

Y1 - 2021

N2 - We consider a convex combination of Volterra cubic stochastic operators defined on a two-dimensional simplex depending on the parameter θ and study their trajectory behaviours. We show that at the values θ = 1/2, the trajectories change their orientation. Moreover, for θ < 1/2 any Volterra cubic stochastic operator has the property being regular and it is non-ergodic while θ > 1/2.

AB - We consider a convex combination of Volterra cubic stochastic operators defined on a two-dimensional simplex depending on the parameter θ and study their trajectory behaviours. We show that at the values θ = 1/2, the trajectories change their orientation. Moreover, for θ < 1/2 any Volterra cubic stochastic operator has the property being regular and it is non-ergodic while θ > 1/2.

KW - Cubic stochastic operator

KW - Quadratic stochastic operator

KW - Volterra operator

UR - https://www.heldermann.de/JCA/JCA28/JCA281/jca28003.htm

UR - https://www.scopus.com/pages/publications/85099642454

M3 - Article

SN - 0944-6532

VL - 28

SP - 19

EP - 30

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 1

ER -

A Family of Volterra Cubic Stochastic Operators

Abstract

Keywords

OECD Field of Science

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