连续时间中的随机优化 下载 mobi epub pdf 电子书 2025

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内容简介

　　"Stochastic optimization in continuous time"（AuthorFwu-Ranq Chang）is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that math-ematical concepts are introduced in a language and terminology familiar to graduate students of economics.

目录

List of Figures
Preface
1 Probability Theory
1.1 Introduction
1.2 Stochastic Processes
1.2.1 In formation Sets and a -Algebras
1.2.2 The Cantor Set
1.2.3 Borel-Cantelli Lemmas
1.2.4 Distribution Functions and Stochastic Processes
1.3 Conditional Expectation
1.3.1 Conditional Probability
1.3.2 Conditional Expectation
1.3,3 Change of Variables
1.4 Notes and Further Readings
2 Wiener Processes
2.1 introduction
2.2 A Heuristic Approach
2.2.1 From Random Walks to Wiener Process
2.2.2 Some Basic Properties of the Wiener Process
2.3 Markov Processes
2.3.1 Introduction
2.3.2 Transition Probability
2.3.3 Diffusion Processes
2.4 Wiener Processes
2.4.1 How to Generate More Wiener Processes
2.4.2 Differentiability of Sample Functions
2.4.3 Stopping Times
2.4.4 The Zero Set
2.4.5 Bounded Variations and the Irregularity of the
Wiener Process
2.5 Notes and Further Readings
3 Stochastic Calculus
3.1 Introduction
3.2 A Heuristic Approach
3.2.1 ls □ （s X ）dWs Riemarm Integrable?
3.2.2 The Choice of□ Matters
3.2.3 In Search of the Class of Functions for a （s, w）
3.3 The Ito Integral
3.3.1 Definition
3.3.2 Martingales
3.4 lto's Lemma: Autonomous Case
3.4.1 Ito's Lemma
3.4.2 Geometric Brownian Motion
3.4.3 Population Dynamics
3.4.4 Additive Shocks or Multiplicative Shocks
3.4.5 Multiple Sources of Uncertainty
3.4.6 Multivariate lto's Lemma
3.5 Ito's Lemma for Time-Dependent Functions
3.5.1 Euler's Homogeneous Differential Equation and the Heat Equation
3.5.2 Black-Scholes Formula
3.5.3 Irreversible Investment
3.5.4 Budget Equation for an Investor
3.5.5 Ito's Lemma: General Form
3.6 Notes and Further Readings
4 Stochastic Dynamic Programming
4.1 Introduction
4.2 Bellman Equation
4.2.1 Infinite-Horizon Problems
4.2.2 Verification Theorem
4.2.3 Finite-Horizon Problems
4.2.4 Existence and Differentiability of the Value Function
4.3 Economic Applications
4.3.1 Consumption and Portfolio Rules
4.3.2 Index Bonds
4.3.3 Exhaustible Resources
4.3.4 Adjustment Costs and （Reversible） Investment
4.3.5 Uncertain Lifetimes and Life Insurance
4.4 Extension: Reeursive Utility
4.4.1 Bellman Equation with Recursive Utility
4.4.2 Effects of Reeursivity: Deterministic Case
4.5 Notes and Further Readings
5 How to Solve it
5.1 Introduction
5.2 HARA Functions
5.2.1 The Meaning of Each Parameter
5.2.2 Closed-Form Representations
5.3 Trial and Error
5.3.1 Linear-Quadratic Models
5.3.2 Linear-HARA models
5.3.3 Linear-Concave Models
5.3,4 Nonlinear-Concave Models
5.4 Symmetry
5.4.1 Linear-Quadratic Model Revisited
5.4.2 Merton's Model Revisited
5.4.3 Fischer's Index Bond Model
5.4.4 Life Insurance
5.5 The Substitution Method
5.6 Martingale Representation Method
5.6.1 Girsanov Transformation
5.6.2 Example: A Portfolio Problem
5.6.3 Which 8 to Choose?
5.6.4 A Transformed Problem
5.7 Inverse Optimum Method
5.7.1 The Inverse Optimal Problem: Certainty Case
5.7.2 The Inverse Optimal Problem: Stochastic Case
5.7.3 Inverse Optimal Problem of Merton's Model
5.8 Notes and Further Readings
6 Boundaries and Absorbing Barriers
6.1 Introduction
6.2 Nonnegativity Constraint
6.2.1 Issues and Problems
6.2.2 Comparison Theorems
6.2.3 Chang and Malliaris's Reflection Method
6.2.4 Inaccessible Boundaries
6.3 Other Constraints
6.3.1 A Portfolio Problem with Borrowing CoosWaints
6.3.2 Viscosity Solutions
6.4 Stopping Rules - Certainty Case
6.4.1 The Baumol-Tobin Model
6.4.2 A Dynamic Model of Money Demand
6.4.3 The Tree-Cutting Problem
6.5 The Expected Discount Factor
6.5.1 Fundamental Equation for Ex[e□]
6.5.2 One Absorbing Barrier
6.5.3 Two Absorbing Barriers
6.6 Optimal Stopping Times
6.6.1 Dynamic and Stochastic Demand for Money
6.6.2 Stochastic Tree-Cutting and Rotation Problems
6.6.3 Investment Timing
6.7 Notes and Further Readings
A Miscellaneous Applications and Exercises
Bibliography
Index

前言/序言

连续时间中的随机优化 下载 mobi epub pdf txt 电子书 格式

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在现代的管理科学、工程技术、社会经济、交通运输、金融保险等诸多领域都存在着大量的最优化问题。与此同时，这些领域又毋庸置疑地存在着人为的模糊性或客观的随机性。然而一个复杂的决策问题通常处在这两种不确定性因素混合的环境之中，模糊随机性就是一种具体的体现。那么，模糊随机环境下如何建立机会测度理论?如何建立单阶段和多阶段模糊随机优化模型?又如何采用逼近方法求解这些优化模型?本书分别回答了这些问题。该书将介绍模糊随机优化理论的最新研究成果，包括模糊随机环境下的平均机会理论、静态模糊随机规划、具有补偿问题的两阶段模糊随机规划、优化模型的逼近方法及其收敛性等问题。本书可作为应用数学专业高年级大学生和运筹学与控制论专业研究生教材，也可作为从事运筹学、管理科学及信息科学研究的高校教师和科技人员的参考书。

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第三：由于无需波前重构，大气湍流带来的闪烁不影响算法的迭代以及反馈装置的数据采集，在大气湍流较强或光束长程传输应用中有其独特优势[3]。

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由于星地链路之间的主要传输介质是大气，穿过路径较长，大气分子对于激光光束的吸收与散射将引起传播方向上光能的衰减，因此传输信道中的大气湍流是限制通信距离及通信系统性能的瓶颈之一，不仅需要考虑大气对激光的吸收与散射，还必须考虑大气的湍流效应。大气湍流会使光载波在传输过程中随机地改变其光束特性，致使携带信息的光波的强度和相位在空间和时间上都呈现随机起伏，造成闪烁现象，极大地降低了系统的成像质量或光束质量。基于随机并行下降算法的自适应光学技术可以提高激光作用到目标上的聚集程度；降低空间目标在望远镜成像面上的模糊程度，提高目标识别的准确度，实现对目标的精跟踪；提高激光通信系统的载波光束质量，降低系统的噪声水平、提高数据传输速率等，在天文自适应成像领域已得到成功应用。

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无需波前传感器的像清晰化技术在不需要波前传感器的条件下，以成像清晰度和接受光能量为性能指标直接作为算法优化的目标函数，优化得到接近理想的校正效果，系统复杂性大大降低，比较适合用于补偿大气湍流带来的闪烁现象。

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