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On the Study of Forward Kolmogorov System and the Corresponding Problems for Inhomogeneous Continuous-Time Markov Chains

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

Abstract

An inhomogeneous continuous-time Markov chain X(t) with finite or countable state space under some natural additional assumptions is considered. As a consequence, we study a number of problems for the corresponding forward Kolmogorov system, which is the linear system of differential equations with special structure of the matrix A(t). In the countable situation we have an equation in the space of sequences \(l_1\). The important properties of X(t) (such as weak and strong ergodicity, perturbation bounds, truncation bounds) are closely connected with behaviour of the solutions of the forward Kolmogorov system as \(t \rightarrow \infty \). The main problems and some approaches for their solution are discussed in the paper.

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Acknowledgements

The research has been supported by the Russian Science Foundation under grant 19-11-00020. The author also would like to thank the organizers of ICDDEA 2019, for their hospitality.

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Authors and Affiliations

  1. Institute of Informatics Problems FRC CSC RAS, Vologda Research Center RAS, Vologda State University, Lenina, 15, Vologda, Russia

    Alexander Zeifman

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  1. Alexander Zeifman
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Correspondence to Alexander Zeifman .

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Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Zeifman, A. (2020). On the Study of Forward Kolmogorov System and the Corresponding Problems for Inhomogeneous Continuous-Time Markov Chains. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_3

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