Applications of two-time-scale markovian systems 本书特色

　　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。

Applications of two-time-scale markovian systems 目录

preface
1 introduction
1.1 two-time-scale markovian systems
1.2 literature review
1.3 why do we need this book?
1.4 outline of the book
part i asymptotic results:two-time-scale markov chains
2 summary of two-time-scale markov chains:finite state spacecases
2.1 two-time-scale continuous-time markov chains
2.2 properties of two-time-scale markov chains
2.2.1 asymptotic expansions
2.2.2 occupation measures
2.2.3 exponential bounds
2.3 ramifications
2.4 notes
3 switching diffusion limits
3.1 introduction
3.2 problem formulation and preliminaries
3.2.1 formulation
3.2.2 conditions
3.2.3 preliminaries
3.3 asymptotic properties
3.3.1 a mean square estimate
3.3.2 weak convergence of the aggregated process
3.4 inclusion of transient states in the jump process
3.5 notes
4 countable state space i:single-group recurrent states
4.1 introduction
4.2 formulation
4.2.1 basic notation
4.2.2 two-time-scale markov chains
4.3 asymptotic expansions
4.3.1 formal expansions
4.3.2 asymptotic justification
4.3.3 asymptotic expansion of transition probability matrices
4.4 occupation measures
4.4.1 second moment bounds and mixing property
4.4.2 functionals of the two-time-scale markov chain
4.4.3 invariance theorem and limit distribution
4.5 applications to queueing processes
4.6 notes
5 countable state space ii:multi-group recurrent states
5.1 introduction
5.2 formulation
5.2.1 notation
5.2.2 queue length and two-time-scale markov chains
5.3 asymptotic properties of probability distribution
5.3.1 formal expansions
5.3.2 asymptotic justification
5.3.3 asymptotic expansion of transition probability matrices
5.4 aggregation and weak convergence
5.5 switching diffusion limit
5.6 an example
5.7 notes
part ii several application examples to financialengineering,insurance,queueing networks,and filtering
6 financial engineering
6.1 geometric brownian motion model
6.2 stock selling rule
6.2.1 two-point boundary value problems
6.2.2 limit problem and near optimality
6.2.3 expected exit time and related probabilities
6.2.4 numerical examples
6.3 near-optimal asset allocation
6.3.1 optimal asset allocation
6.3.2 convergence of value functions
6.3.3 near-optimal asset allocation
6.4 notes
7 near-optimal dividend policy
7.1 formulation
7.2 limit problem
7.3 convergence of the cost and value functions
7.4 near-optimal dividend policy
7.5 notes
8 queueing networks
8.1 application to m_t/m_t/1/m
8.2 markovian queueing networks
8.3 markov-modulated-rate fluid models
8.4 notes
9 wonham filtering
9.1 introduction
9.1.1 wonham filtering
9.2 two-time scale markov chains
9.2.1 two-time-scale filters
9.3 limit filter and two-time-scale approximation
9.3.1 limit filter
9.3.2 two-time-scale approximation
9.4 a numerical example
9.5 inclusion of transient states
9.6 notes
a background materials
references
index

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自然科学 数学 概率论与数理统计

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