A Family of Volterra Cubic Stochastic Operators

Uygun Jamilov; Andrejs Reinfelds

A Family of Volterra Cubic Stochastic Operators

Uygun Jamilov
, Andrejs Reinfelds

Matemātikas nodaļa

Academy of Sciences of the Republic of Uzbekistan

Zinātniskās darbības rezultāts: Devums žurnālam › Zinātniskais raksts (žurnālā) › koleģiāli recenzēts

18 Atsauces (Scopus)

Kopsavilkums

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.

Oriģinālvaloda	Angļu
Lapas (no-līdz)	19-30
Lapu skaits	12
Žurnāls	Journal of Convex Analysis
Sējums	28
Izdevuma numurs	1
Publikācijas statuss	Publicēts - 2021

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@article{079396c51475412ea62e84c3b5fe83ac,

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.",

keywords = "Cubic stochastic operator, Quadratic stochastic operator, Volterra operator",

author = "Uygun Jamilov and Andrejs Reinfelds",

note = "Publisher Copyright: {\textcopyright} Heldermann Verlag",

year = "2021",

language = "English",

volume = "28",

pages = "19--30",

journal = "Journal of Convex Analysis",

issn = "0944-6532",

publisher = "Heldermann Verlag",

number = "1",

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TY - JOUR

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

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