Existence of a unique invariant measure for a class of equicontinuous Markov operators with application to a stochastic model for an autoregulated gene
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Publication:502749
DOI10.5802/ambp.360zbMath1353.92042OpenAlexW2561080682MaRDI QIDQ502749
Katarzyna Horbacz, Tomasz Szarek, Sander Cornelis Hille
Publication date: 6 January 2017
Published in: Annales Mathématiques Blaise Pascal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.5802/ambp.360
Markov semigroups and applications to diffusion processes (47D07) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Biochemistry, molecular biology (92C40)
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Cites Work
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- Qualitative simulation of the initiation of sporulation in \textit{Bacillus subtilis}
- The mean and noise of protein numbers in stochastic gene expression
- On a unique ergodicity of some Markov processes
- Feller processes on nonlocally compact spaces
- On ergodicity of some Markov processes
- Semigroups of linear operators and applications to partial differential equations
- Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
- Cell division and the stability of cellular populations
- The mean frequency of transcriptional bursting and its variation in single cells
- Noise in genetic and neural networks
- On the Existence of Invariant Measures for Piecewise Monotonic Transformations
- Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations
- Invariant measures for nonexpansive Markov operators on Polish spaces
- Ergodicity for Infinite Dimensional Systems
- A note on a theorem of Karlin
- Molecular distributions in gene regulatory dynamics
