TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

On the discrete and continuous Markov processes

*

* Corresponding author · click or hover a name for details

pp. 1901–1908Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2160XML
Received:
14 May 2024
Published Online:
14 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2160
Pages:
1901–1908

Abstract

The discrete and continuous Markov processes and Markov chains are considered. Basic concepts are introduced, and some applications of Markov processes are considered.

Keywords

Subject Classifications

60J0560J1060J2060J2260J2560J2760J2890C40

References

[1] D. Bakry, I. Gentil, and M. Ledoux, Analysis and Geometry of Markov Diffusion Operators, Grundlehren der mathematischen Wissenschaften, vol. 348, Springer, Cham-Heidelberg-New York-Dordrecht-London (2014). 
[2] M. Chen, From Markov Chains to Non-Equilibrium Particle Systems, 2nd ed., World Scientific, Singapore (2004). 
[3] S. N. Ethier, and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley Series in Probability and Statistics, John Wiley & Sons, Hoboken, NJ (2005). 
[4] G. L. Jones, “On the Markov chain central limit theorem”, Probability Surveys, vol. 1, pp. 299-320 (2004). 
[5] C. Landim, “Central limit theorem for Markov processes”, in From Classical to Modern Probability, Pierre Picco and Jaime San Mastin (eds.), Progress in Probability, vol. 54, Birkhauser, Basel, pp. 145-205 (2003). 
[6] T. M. Liggett, Continuous Time Markov Processes: An Introduction, Graduate Studies in Mathematics, vol. 113, American Mathematical Society, Providence, RI (2010). 
[7] S. Meyn, and R. L. Tweedie, Markov Chains and Stochastic Stability, 2nd ed., Cambridge University Press, Cambridge (2009). 
[8] G. O. Roberts, and J. S. Rosenthal, “General state space Markov chains and MCMC algorithms”, Probability Surveys, vol. 1, pp. 20-71 (2004). 
[9] L. C. G. Rogers, and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. 1 Foundations, Cambridge Mathematical Library, Cambridge University Press, Cambridge (2000). 
[10] L. C. G. Rogers, and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. 2 Itô Calculus, Cambridge Mathematical Library, Cambridge University Press, Cambridge (2000). 
[11] S. M. Stefanov, “On the implementation of stochastic quasigradient methods to some facility location problems”, Yugoslav Journal of Operations Research, vol. 10, no. 2, pp. 235-256 (2000). 
[12] S. M. Stefanov, “Convex separable minimization subject to bounded variables”, Computational Optimization and Applications. An International Journal, vol. 18, no. 1, pp. 27-48 (2001). 
[13] S. M. Stefanov, Separable Programming: Theory and Methods, Applied Optimization, vol. 53, Kluwer Academic Publishers, Dordrecht-Boston-London (2001). 
[14] S. M. Stefanov, “Minimization of a convex linear-fractional separable function subject to a convex inequality constraint or linear equality constraint and bounds on the variables”, Applied Mathematics Research Express AMRX, vol. 2006, no. 4, pp. 1-24 (2006) Article ID 36581. 
[15] S. M. Stefanov, “Minimization of a strictly convex separable function subject to convex separable inequality constraint and box constraints”, Journal of Interdisciplinary Mathematics, vol. 12, no. 5, pp. 647-673 (2009). 
[16] S. M. Stefanov, “Solution of some convex separable resource allocation and production planning problems with bounds on the variables”, Journal of Interdisciplinary Mathematics, vol. 13, no. 5, pp. 541-569 (2010). 
[17] S. M. Stefanov, “Well-posedness and primal-dual analysis of some convex separable optimization problems”, Advances in Operations Research, vol. 2013, 10 pp. (2013) Article ID 279030. 
[18] S. M. Stefanov, “Strictly convex separable optimization with linear equality constraints and bounded variables”, Journal of Statistics and Management Systems, vol. 21, no. 2, pp. 261-272 (2018). 
[19] S. M. Stefanov, “Characterization of the optimal solution of the convex separable continuous knapsack problem and related problems”, Journal of Information and Optimization Sciences, vol. 42, no. 1, pp. 1-16 (2021). 
[20] S. M. Stefanov, “On the numerical solution of separable stochastic inventory control problems”, Journal of Information and Optimization Sciences, vol. 42, no. 3, pp. 533-561 (2021). 
[21] S. M. Stefanov, Separable Optimization: Theory and Methods, Springer Optimization and Its Applications, vol. 177, Springer, Cham (2021). 
[22] S. M. Stefanov, “On the solution of quadratic programming problems”, Journal of Information and Optimization Sciences, vol. 44, no. 2, pp. 243-253 (2023). 
[23] S. M. Stefanov, “Continuous linear knapsack problems revisited”, Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023). 
[24] S. M. Stefanov, “Numerical solution of box constrained separable convex quadratic programming problems”, Journal of Information and Optimization Sciences, vol. 45, no. 1, pp. 57-71 (2024). 
[25] S. M. Stefanov, “Linear programming problems and matrix games”, Journal of Interdisciplinary Mathematics, vol. 27, no. 1, pp. 57-65 (2024). 
[26] S. M. Stefanov, “On the solution of two-person zero-sum matrix games”, Journal of Information and Optimization Sciences, vol. 45, no. 3, pp. 649-657 (2024). 
[27] S. M. Stefanov, “On the queueing theory problems and applications”, Journal of Statistics and Management Systems, to appear. 
[28] Q. Wang, M. Kageyama, and J. Zhang, “New evaluation criteria in the Markov decision processes”, Journal of Statistics and Management Systems, vol. 24, no. 3, pp. 625–-632 (2021).

Views: 233Downloads: 152Citations: 0