Applications of two-time-scale markovian systems
本书特色
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本书主要包含两部分。**部分是马尔可夫系统的渐近性质。首先回顾了已有的关于双时间尺度、有限状态马尔可夫系统的结果，然后集中讨论了在双时间尺度框架下，具有可数状态空间的马尔可夫系统和切换扩散系统的渐近性质。同时考虑了具有广泛应用背景、其生成算子也依赖于系统状态本身的此两类系统的渐近性质。书中第二部分集中讨论了这两类系统在随机制造业、排队网络、金融工程、保险与风险管理等领域的应用。为了便于阅读，书中每个章节相对独立。本书致力于对以随机制造业、排队网络、金融工程、保险与风险管理、过程控制的wonham滤波等不同领域的实际应用为背景、具有双时间尺度这一共同特性、大规模复杂随机系统的优化与控制问题的理论研究。希望本书对马尔可夫系统的建模、分析、优化、仿真和控制有一定的参考价值。
本书可作为应用数学、应用概率和运筹与控制领域专家、学者和研究生的参考书。
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作者简介
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G.George Yin
Department of Mathematics
Wayne State University
Detroit,MI 48202,U.S.A.
gyin@math.wayne.edu
Qing Zhang
Department of Mathematics
University of Georgia
Athens,GA 30602,U.S.A.
qingz@math.uga.edu
Hanqin Zhang
Academy of Mathematics and
Systems Science,Academia Sinica
Beijing,100190,China
hanqin@amt.cn.ac
and
NUS Business School
National University of Singapore
Singapore,117592
bizzhq@nus.edu.sg
]
目录
preface1 introduction1.1 two-time-scale markovian systems1.2 literature review1.3 why do we need this book?1.4 outline of the bookpart i asymptotic results:two-time-scale markov chains2 summary of two-time-scale markov chains:finite state spacecases2.1 two-time-scale continuous-time markov chains2.2 properties of two-time-scale markov chains2.2.1 asymptotic expansions2.2.2 occupation measures2.2.3 exponential bounds2.3 ramifications2.4 notes3 switching diffusion limits3.1 introduction3.2 problem formulation and preliminaries3.2.1 formulation3.2.2 conditions3.2.3 preliminaries3.3 asymptotic properties3.3.1 a mean square estimate3.3.2 weak convergence of the aggregated process3.4 inclusion of transient states in the jump process3.5 notes4 countable state space i:single-group recurrent states4.1 introduction4.2 formulation4.2.1 basic notation4.2.2 two-time-scale markov chains4.3 asymptotic expansions4.3.1 formal expansions4.3.2 asymptotic justification4.3.3 asymptotic expansion of transition probability matrices4.4 occupation measures4.4.1 second moment bounds and mixing property4.4.2 functionals of the two-time-scale markov chain4.4.3 invariance theorem and limit distribution4.5 applications to queueing processes4.6 notes5 countable state space ii:multi-group recurrent states5.1 introduction5.2 formulation5.2.1 notation5.2.2 queue length and two-time-scale markov chains5.3 asymptotic properties of probability distribution5.3.1 formal expansions5.3.2 asymptotic justification5.3.3 asymptotic expansion of transition probability matrices5.4 aggregation and weak convergence5.5 switching diffusion limit5.6 an example5.7 notespart ii several application examples to financialengineering,insurance,queueing networks,and filtering6 financial engineering6.1 geometric brownian motion model6.2 stock selling rule6.2.1 two-point boundary value problems6.2.2 limit problem and near optimality6.2.3 expected exit time and related probabilities6.2.4 numerical examples6.3 near-optimal asset allocation6.3.1 optimal asset allocation6.3.2 convergence of value functions6.3.3 near-optimal asset allocation6.4 notes7 near-optimal dividend policy7.1 formulation7.2 limit problem7.3 convergence of the cost and value functions7.4 near-optimal dividend policy7.5 notes8 queueing networks8.1 application to mt/mt/1/m8.2 markovian queueing networks8.3 markov-modulated-rate fluid models8.4 notes9 wonham filtering9.1 introduction9.1.1 wonham filtering9.2 two-time scale markov chains9.2.1 two-time-scale filters9.3 limit filter and two-time-scale approximation9.3.1 limit filter9.3.2 two-time-scale approximation9.4 a numerical example9.5 inclusion of transient states9.6 notesa background materialsreferencesindex
封面
书名:Applications of two-time-scale markovian systems
作者:殷刚
页数:207
定价:¥80.0
出版社:科学出版社
出版日期:2013-05-01
ISBN:9787030373496
PDF电子书大小:102MB 高清扫描完整版