.svg){kind=logo}
ON NON-REVERSIBLE CIRCUIT CHAINS
Keywords:
circuit chain, directed weighted circuit, non-reversible Markov chain, random walk, fixed environmentDOI:
https://doi.org/10.17654/0974165825044Abstract
Regarding the context of circuit representation theory of Markov processes, we study the alternative unique representation by directed circuits and weights of the corresponding non-reversible Markov chain describing a random walk with steps (+3) or (–2), as an application of the existence of non-reversible circuit chains.
Received: July 2, 2025
Revised: July 27, 2025
Accepted: July 31, 2025
References
[1] Yv. Derriennic, Random walks with jumps in random environments (examples of cycle and weight representations), Probability Theory and Mathematical Statistics: Proceedings of the 7th Vilnius Conference on Probability Theory and Mathematical Statistics, De Gruyter Brill, 1999, pp. 199-212.
[2] Ch. Ganatsiou, On cycle representations of random walks in fixed, random environments, 58th World Congress of the International Statistical Institute, Dublin, 2011.
[3] Ch. Ganatsiou, On the study of transience and recurrence of the Markov chain defined by directed weighted circuits associated with a random walk in fixed environment, J. Prob. Stat. (2013), Article ID 424601.
[4] Ch. Ganatsiou, On cycle representations of discrete-time birth-death processes, 29th European Meeting of Statisticians, Budapest, 2013.
[5] Ch. Ganatsiou et al, On discrete-time birth-death processes defined by directed weighted circuits, JP J. Biostatistics 11(2) (2014), 103-116.
[6] Ch. Ganatsiou et al, On the study of discrete-time birth-death circuit chains in random ergodic environments, JP J. Biostatistics 11(2) (2014), 157-168.
[7] Ch. Ganatsiou, On the criteria of transience and recurrence for the discrete-time birth death chains defined by directed circuits and weights in random ergodic environments, JP J. Biostatistics 13(2) (2016), 103-117.
[8] Ch. Ganatsiou, On the study of circuit chains associated with a random walk with jumps in fixed, random environments, 7th European Congress of Mathematics, Berlin, 2016.
[9] Ch. Ganatsiou, On the expected extinction time for the adjoint birth-death circuit chains in random environments, 32nd European Meeting of Statisticians, Palermo, 2019.
[10] Ch. Ganatsiou, On the study of circuit chains associated with a random walk with jumps in fixed, random environments: criteria of recurrence and transience, Mathematical Analysis and Applications, Springer Optimization and Its Applications, Springer, Vol. 154, 2019, pp. 185-203.
[11] Ch. Ganatsiou, On the study of extinction of circuit chains describing random walks in random environments, 63rd World Congress of the International Statistical Institute (Virtual), Hague, 2021.
[12] Ch. Ganatsiou, On irreducible denumerable continuous parameter circuit chains: analysis of a generalized sample path case, Quaest. Math. 45(1) (2022), 41-53.
[13] Ch. Ganatsiou, On the approximation of extinction time for the discrete-time birth-death circuit chains in random environments, Approximation and Computation in Science and Engineering, Springer, 2022, pp. 333-348.
[14] Ch. Ganatsiou, On the expected extinction time of the adjoint circuit chains associated with a random walk with jumps in random environments, High Dimensional Optimization and Probability: With a View Towards Data Sciences, Springer, 2022, pp. 219-239.
[15] Ch. Ganatsiou, On birth-death circuit chains in fixed environments: analysis of a generalized sample path case, 34th European Meeting of Statisticians (EMS-2023), Warsaw, 2023.
[16] Ch. Ganatsiou and Savvas K. Ilias, On the study of circuit chains describing a random walk with jumps in fixed environments: a generalized sample path case, in Global Optimization, Computation, Approximation and Applications, World Scientific Publishing Press, 2025 (to appear).
[17] Ch. Ganatsiou, On the stochastic properties of birth-death circuit chains for a generalized sample path case, Mathematical Analysis, Optimization, Approximation and Applications, World Scientific Publishing Press, 2025 (to appear).
[18] Ch. Ganatsiou, Savvas K. Ilias and A. Xenakis, On the study of cycle chains representing nonreversible Markov chains associated with random walks with jumps in fixed environments, Optimization, Discrete Mathematics and Applications to Data Sciences, Springer 2025, pp. 91-103.
[19] Ch. Ganatsiou and Savvas K. Ilias, On the study of cycle chains associated with non-reversible Markov chains describing a random walk with jumps in random environments, Trends in Applied Mathematical Analysis, Springer, 2026 (to appear).
[20] Ch. Ganatsiou, On circuit and weight representation of the embedded Markov chain in the M/G/1 queuing system, Mathematical Analysis, Optimization and Data Sciences, World Scientific Publishing Press, 2026 (to appear).
[21] D. B. Hughes, Random Walks and Random Environments, Volume I: Random Walks, Oxford University Press, 1995.
[22] S. Kalpazidou, Cycle Representations of Markov Processes, Springer, 1995.
[23] J. MacQueen, Circuit processes, Ann. Probab. 9 (1981), 604-610.
[24] Qian Minning and Qian Min, Circulation for recurrent Markov chains, Z. Wahrsch. Verw. Gebiete 59(2) (1982), 203-210.
[25] K. Pearson, The problem of the random walk, Nature 72 (1905), 294.
[26] F. Spitzer, Principles of Random Walks, 2nd ed., Springer, 1976.
[27] A. H. Zemanian, Infinite Electrical Networks, Cambridge University Press, 1991.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
