This article is cited in 15 papers

Doubly stochastic operators on a finite-dimensional simplex

F. A. Shahidi

National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: Generalizing the concept of a quadratic doubly stochastic operator, we introduce the concept of an arbitrary doubly stochastic operator. We give a necessary condition for double stochasticity. Moreover, we prove an ergodic theorem for doubly stochastic operators.

Keywords: stochastic operator, doubly stochastic operator, ergodic theorem.

UDC: 517.98+519.218.84

Received: 20.12.2007

 English version: Siberian Mathematical Journal, 2009, 50:2, 368–372

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