A dynamic programming approach for finite Markov processes and algorithms for the calculation of the limit matrix in Markov chains

Stefan Pickl; Dmitrii Lozovanu

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A dynamic programming approach for finite Markov processes and algorithms for the calculation of the limit matrix in Markov chains

机译：有限马尔可夫过程的动态规划方法和马尔可夫链中极限矩阵的计算算法

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摘要

New calculation procedures for finding the probabilities of state transitions of the system in discrete Markov processes based on dynamic programming are developed and polynomial time algorithms for determining the limit state matrix in such processes are proposed. Computational complexity aspects and possible applications of the proposed algorithms for the stochastic optimization problems are characterized.

机译：提出了一种基于动态规划的离散马尔可夫过程寻找系统状态转移概率的新计算程序，并提出了确定过程中极限状态矩阵的多项式时间算法。表征了计算复杂性方面以及所提出算法用于随机优化问题的可能应用。

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《Optimization: A Journal of Mathematical Programming and Operations Research》 |2011年第12期|共20页
作者
Stefan Pickl; Dmitrii Lozovanu;
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正文语种 eng
中图分类应用数学;
关键词
Discrete Markov process; Probability of state transition; Limit state matrix; Dynamic programming; Polynomial time algorithm;

机译：离散马尔可夫过程状态转移概率极限状态矩阵动态规划多项式时间算法;

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专利

1. A dynamic programming approach for finite Markov processes and algorithms for the calculation of the limit matrix in Markov chains [J] . Stefan Pickl, Dmitrii Lozovanu Optimization: A Journal of Mathematical Programming and Operations Research . 2011,第10a12期

机译：有限马尔可夫过程的动态规划方法和马尔可夫链中极限矩阵的计算算法
2. A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming [J] . Arlotto Alessandro, Steele J. Michael Mathematics of operations research . 2016,第4期

机译：临时非齐次马尔可夫链的中心极限定理及其在动态规划中的应用
3. New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system [J] . Ohno Katsuhisa, Boh Toshitaka, Nakade Koichi, European Journal of Operational Research . 2016,第1期

机译：用于大规模无折扣马尔可夫决策过程的新的近似动态规划算法及其在优化生产和分销系统中的应用
4. A Dynamic Programming Approach for Ambient Intelligence Platforms in Running Sports Based on Markov Decision Processes [C] . J. Vales-Alonso, P. López-Matencio, J. J. Alcaraz, International Human System Interaction Conference . 2012

机译：基于马尔可夫决策过程的运行运动中的环境智能平台动态编程方法
5. DYNAMIC PROBABILISTIC SYSTEMS WITH CONTINUOUS PARAMETER MARKOV CHAINS AND SEMI-MARKOV PROCESSES. [D] . LEE, CHRISTOPHER TIN HTUN. 1973

机译：具有连续参数马尔可夫链和半马尔可夫过程的动态概率系统。
6. Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution [O] . Regina Finsterhölzl, Manuel Katzer, Andreas Knorr, 2020

机译：使用Matrix-Master状态用于开放量子的多体系统：Markovian和非马尔可维亚时演变的有效算法
7. A Central Limit Theorem for Temporally Non-Homogenous Markov Chains with Applications to Dynamic Programming [O] . Arlotto, Alessandro, Steele, J Michael 2016

机译：临时非齐次马尔可夫链的中心极限定理及其在动态规划中的应用
8. Row-Continuous Finite Markov Chains, Structure and Algorithms [R] . Keilson, J., Sumita, U., Zachmann, M. 1981

机译：行连续有限马氏链，结构和算法

A dynamic programming approach for finite Markov processes and algorithms for the calculation of the limit matrix in Markov chains

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