On quadratic stochastic processes and related differential equations

Mukhamedov, Farrukh; Supar, Nurul Akma; Hee, Pah Chin

doi:10.1088/1742-6596/435/1/012013

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Next goal of the paper is to define cubic stochastic processes (CSP) and give differential equations for such processes. This investigations will be similar to works [8], [20,21], [24]- [26], where the authors introduced a continuous-time dynamical system as quadratic stochastic processes (QSP). The reader is referred to very recent book [19] for the theory of QSPs.…”

Section: Introductionsupporting

confidence: 64%

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On cubic stochastic operators and processes

Mamurov

Rozikov

2016

J. Phys.: Conf. Ser.

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In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The measurable space can be given on a finite or continual set. The finite case has been investigated before. So here we mainly work on the continual set. We give a construction of a CSO and show that dynamical systems generated by such a CSO can be studied by studying of the behavior of trajectories of a CSO given on a finite dimensional simplex. We define a CSP and drive differential equations for such CSPs with continuous time.

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Section: Introductionsupporting

confidence: 64%

“…The equation (2.2) in Definition 2.2 is an analogue of Chapman-Kolmogorov equation. In [8], [21], [24]- [26] such equations were extended to QSPs. We note that for QSPs there are two types of the Chapman-Kolmogorov equations: type A and type B.…”

Section: Definitions and Examplesmentioning

confidence: 99%