《雙時間尺度的馬爾可夫系統的套用》是2013年在科學出版社出版的圖書，該書作者是]G.George Yin, Hanqin Zhang, Qinqing Zhang等。
基本介紹
- 書名：雙時間尺度的馬爾可夫系統的套用
- 作者：]G.George Yin, Hanqin Zhang, Qinqing Zhang等
- ISBN：9787030373496
- 類別：理論專著/研究生教育
- 頁數：224頁
- 定價：80.00元
- 出版社：科學出版社
- 出版時間：2013-5
- 裝幀：平裝
- 開本：B5
- 語種：英文
- 字數：343千字
內容簡介,適用對象,目錄,
內容簡介
本書主要包含兩部分。第一部分是馬爾可夫系統的漸近性質。首先回顧了已有的關於雙時間尺度、有限狀態馬爾可夫系統的結果，然後集中討論了在雙時間尺度框架下，具有可數狀態空間的馬爾可夫系統和切換擴散系統的漸近性質。同時考慮了具有廣泛套用背景、其生成運算元也依賴於系統狀態本身的此兩類系統的漸近性質。書中第二部分集中討論了這兩類系統在隨機製造業、排隊網路、金融工程、保險與風險管理等領域的套用。為了便於閱讀，書中每個章節相對獨立。本書致力於對以隨機製造業、排隊網路、金融工程、保險與風險管理、過程控制的Wonham濾波等不同領域的實際套用為背景、具有雙時間尺度這一共同特性、大規模複雜隨機系統的最佳化與控制問題的理論研究。希望本書對馬爾可夫系統的建模、分析、最佳化、仿真和控制有一定的參考價值。
適用對象
本書可作為套用數學、套用機率和運籌與控制領域專家、學者和研究生的參考書。
目錄
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 Space Cases
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 Financial Engineering,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 Mt/Mt/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
