Conditional law of large numbers and entropy of Markov processes

Chen Jinwen; Dan Sen

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Conditional law of large numbers and entropy of Markov processes

机译：马尔可夫流程的大数和熵的条件法

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摘要

The importance of a law of large numbers is well known. In this paper, conditional law of large numbers for Markov processes is proved, which can be used in computing quantities related to sub-Markov sequences. A variational interpretation for this limit is given, which shows that typically the quantities of interests tend to minimize a certain entropy. A quasi-compact operator argument is involved.

机译：大量法则的重要性是众所周知的。在本文中，证明了马尔可夫工艺的大量条件法，其可用于计算与亚马尔可夫序列相关的数量。给出了对该限制的变分解释，这表明通常利益的数量倾向于最小化一定的熵。涉及准紧凑的操作员参数。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2020年第2期|共15页
作者
Chen Jinwen; Dan Sen;
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作者单位

Tsinghua Univ Dept Math Sci Beijing Peoples R China;

Tsinghua Univ Dept Math Sci Beijing Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
Markov process; conditional limit; conditional law of large numbers; entropy; quasi-compact operator;

机译：马尔可夫进程;条件限制;大量条件规律;熵;准紧凑型操作员;

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专利

1. Conditional law of large numbers and entropy of Markov processes [J] . Chen Jinwen, Dan Sen Infinite dimensional analysis, quantum probability, and related topics . 2020,第2期

机译：马尔可夫流程的大数和熵的条件法
2. THE STABILITY OF CONDITIONAL MARKOV PROCESSES ANDMARKOV CHAINS IN RANDOM ENVIRONMENTS [J] . RAMON VAN HANDEL The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics . 2009,第5期

机译：随机环境中条件马尔可夫过程和马尔可夫链的稳定性
3. Entropy Maximization for Markov and Semi-Markov Processes [J] . Valerie Girardin Methodology and computing in applied probability . 2004,第1期

机译：马尔可夫和半马尔可夫过程的熵最大化
4. Markov and Conditionally Markov Processes: from Gaussian to Elliptical [C] . Mengjiao Tang, Yao Rong, X. Rong Li International Conference on Information Fusion . 2019

机译：马尔可夫过程和有条件马尔可夫过程：从高斯到椭圆
5. Extremal Entropy: Information Geometry, Numerical Entropy Mapping, and Machine Learning Application of Associated Conditional Independences. [D] . Liu, Yunshu. 2016

机译：极值熵：信息几何，数值熵映射和相关条件独立性的机器学习应用。
6. Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir [O] . Dong Wang, Ai-Jun Huang, Ross D. Hoehn, -1

机译：结构化储层下马尔可夫过程和非马尔可夫过程的熵不确定关系
7. The stability of conditional Markov processes and Markov chains in random environments [O] . van Handel, Ramon 2009

机译：条件马尔可夫过程和马尔可夫链的稳定性随机环境

Conditional law of large numbers and entropy of Markov processes

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