On the discrete and continuous Markov processes
*Stefan M. StefanovCorresponding authorstefm@swu.bgDepartment of InformaticsNeofit Rilski South-West UniversityBlagoevgrad, 2700, BulgariaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 14 May 2024
- Published Online:
- 14 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2160
- Pages:
- 1901–1908
Abstract
Keywords
Subject Classifications
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).




