On the ergodic principle for Markov and quadratic stochastic processes and its relations

DOI10.1016/j.laa.2005.12.032zbMath1096.60038arXivmath/0511270OpenAlexW1964219582MaRDI QIDQ2496643

Farrukh Mukhamedov, Hasan Akin, Nasir N. Ganikhodjaev

Publication date: 20 July 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511270

zbMATH Keywords

Markov processes

Mathematics Subject Classification ID

Chemistry (92E99) Discrete-time Markov processes on general state spaces (60J05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Ergodic theory of linear operators (47A35) Random dynamical systems (37H99) Limit theorems in probability theory (60F99)

Related Items (15)

On \(L_1\)-weak ergodicity of nonhomogeneous discrete Markov processes and its applications ⋮ Ergodicity of non-homogeneous \(\mathbf{p}\)-majorizing quadratic stochastic operators ⋮ Projective surjectivity of quadratic stochastic operators on \(L^1\) and its application ⋮ Ergodicity of nonlinear Markov operators on the finite dimensional space ⋮ Krause mean processes generated by cubic stochastic diagonally primitive matrices ⋮ Prevalence problem in the set of quadratic stochastic operators acting on \(L^{1}\) ⋮ Krause mean processes generated by cubic stochastic matrices IV: off-diagonally uniformly positive nonautonomous cubic stochastic matrices ⋮ On the mixing property and the ergodic principle for nonhomogeneous Markov chains ⋮ Applications of quadratic stochastic operators to nonlinear consensus problems ⋮ QUADRATIC STOCHASTIC OPERATORS AND PROCESSES: RESULTS AND OPEN PROBLEMS ⋮ A chain of evolution algebras ⋮ Reaching a consensus via Krause mean processes in multi-agent systems: quadratic stochastic operators ⋮ On mixing of Markov measures associated with b−bistochastic QSOs ⋮ Ergodicity of $p$-majorizing nonlinear Markov operators on the finite dimensional space ⋮ On marginal processes of quadratic stochastic processes

Cites Work

• Analytic methods in the theory of quadric stochastic operators
• On stochastic processes generated by quadric operators
• Quadratic differential systems for interactive population models
• Ergodic properties of discrete quadratic stochastic processes defined on von Neumann algebras
• Quadratic transformations: a model for population growth. I
• On the ergodic principle for Markov processes associated with quantum quadratic stochastic processes
• Theory of operator algebras I.
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