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Stochastic Control Theory : Dynamic Programming Principle, Paperback by Nisio...

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Objectstaat
Vrijwel nieuw: Een boek dat er als nieuw uitziet, maar al wel is gelezen. De kaft is niet zichtbaar ...
Book Title
Stochastic Control Theory : Dynamic Programming Principle
ISBN
9784431564089
Publication Name
Stochastic Control Theory : Dynamic Programming Principle
Item Length
9.2in
Publisher
Springer Japan
Publication Year
2016
Series
Probability Theory and Stochastic Modelling Ser.
Type
Textbook
Format
Trade Paperback
Language
English
Item Height
0.6in
Author
Makiko Nisio
Item Width
6.1in
Item Weight
144.7 Oz
Number of Pages
Xv, 250 Pages

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Product Information

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 aone-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.

Product Identifiers

Publisher
Springer Japan
ISBN-10
443156408x
ISBN-13
9784431564089
eBay Product ID (ePID)
19038682359

Product Key Features

Author
Makiko Nisio
Publication Name
Stochastic Control Theory : Dynamic Programming Principle
Format
Trade Paperback
Language
English
Publication Year
2016
Series
Probability Theory and Stochastic Modelling Ser.
Type
Textbook
Number of Pages
Xv, 250 Pages

Dimensions

Item Length
9.2in
Item Height
0.6in
Item Width
6.1in
Item Weight
144.7 Oz

Additional Product Features

Series Volume Number
72
Number of Volumes
1 Vol.
Lc Classification Number
Qa273.A1-274.9
Edition Number
2
Copyright Date
2015
Topic
Differential Equations / General, Functional Analysis, Probability & Statistics / Stochastic Processes, Probability & Statistics / General
Dewey Decimal
003.76
Intended Audience
Trade
Dewey Edition
23
Illustrated
Yes
Genre
Mathematics

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The book was stated as good condition but, the listing didn't state it was a library book. It has library cards and stickers. It wasn't packed as well as it could have been. The bottom of the hardback was bent. That should have been noted in the description. Fast shipping.
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