QQ登录

只需一步,快速开始

 找回密码
 注册

QQ登录

只需一步,快速开始

查看: 1228|回复: 10

Springer2015,Stochastic Control Theory: Dynamic Programming Principle 2ed.pdf

[复制链接]
  • TA的每日心情
    开心
    2016-3-19 06:18
  • 签到天数: 18 天

    [LV.4]偶尔看看III

    发表于 2015-2-25 12:51:48 | 显示全部楼层 |阅读模式
    f5093adef475895b221b3461c663d60f-d.jpg
    高清版本pdf 回复可见
    游客,如果您要查看本帖隐藏内容请回复


    This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems.

    First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem.

    Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations.

    Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions.

    This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
    Table of contents :

    Content:
    Front Matter....Pages i-xv
    Stochastic Differential Equations....Pages 1-30
    Optimal Control for Diffusion Processes....Pages 31-78
    Viscosity Solutions for HJB Equations....Pages 79-115
    Stochastic Differential Games....Pages 117-151
    Stochastic Parabolic Equations....Pages 153-207
    Optimal Controls for Zakai Equations....Pages 209-244
    Back Matter....Pages 245-250

    回复

    使用道具 举报

  • TA的每日心情
    开心
    2016-4-4 15:42
  • 签到天数: 6 天

    [LV.2]偶尔看看I

    发表于 2015-10-4 13:45:05 | 显示全部楼层
    经典好书,推荐一个
    回复 支持 反对

    使用道具 举报

  • TA的每日心情
    开心
    2017-12-15 11:07
  • 签到天数: 161 天

    [LV.7]常住居民III

    发表于 2015-10-29 00:21:41 | 显示全部楼层
    随机控制,不能错过!
    回复 支持 反对

    使用道具 举报

  • TA的每日心情
    难过
    2019-3-27 12:57
  • 签到天数: 63 天

    [LV.6]常住居民II

    发表于 2016-5-7 21:21:57 | 显示全部楼层
    thanks for sharing
    回复 支持 反对

    使用道具 举报

  • TA的每日心情
    开心
    2019-4-13 17:18
  • 签到天数: 35 天

    [LV.5]常住居民I

    发表于 2017-12-22 09:24:37 | 显示全部楼层
    非常感谢楼主分享
    回复 支持 反对

    使用道具 举报

    该用户从未签到

    发表于 2017-12-26 12:56:40 | 显示全部楼层
    Stochastic Calculus: An Introduction Through Theory and Exercises pdf
    回复 支持 反对

    使用道具 举报

  • TA的每日心情
    开心
    2017-9-16 23:04
  • 签到天数: 13 天

    [LV.3]偶尔看看II

    发表于 2017-12-30 19:05:39 | 显示全部楼层
    66666666666666666
    回复 支持 反对

    使用道具 举报

    该用户从未签到

    发表于 2018-7-26 18:12:02 | 显示全部楼层
    经典好书,看看
    回复 支持 反对

    使用道具 举报

  • TA的每日心情
    郁闷
    2018-9-13 07:06
  • 签到天数: 42 天

    [LV.5]常住居民I

    发表于 2018-11-9 08:43:34 | 显示全部楼层
    非常感谢分享
    回复 支持 反对

    使用道具 举报

    您需要登录后才可以回帖 登录 | 注册

    本版积分规则

        
      小黑屋|手机版|Archiver|( 鄂ICP备16007464号 )

    GMT+8, 2019-8-24 03:53 , Processed in 0.263126 second(s), 24 queries .

    © 2001-2011 Powered by Discuz! X3.2. Theme By Yeei! Licensed

    快速回复 返回顶部 返回列表