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Makiko Nisio Stochastic Control Theory (Hardback) (UK IMPORT)

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Specificaties

Objectstaat
Nieuw: Een nieuw, ongelezen en ongebruikt boek in perfecte staat waarin geen bladzijden ontbreken of ...
Book Title
Stochastic Control Theory
Title
Stochastic Control Theory
Subtitle
Dynamic Programming Principle
EAN
9784431551225
ISBN
9784431551225
Edition
2nd ed. 2015
Genre
Science Nature & Math
Release Year
2014
Release Date
12/09/2014
Country/Region of Manufacture
JP
Item Height
235mm
Publication Year
2014
Series
Probability Theory and Stochastic Modelling Ser.
Type
Textbook
Format
Hardcover
Language
English
Publication Name
Stochastic Control Theory : Dynamic Programming Principle
Author
Makiko Nisio
Item Length
9.3in
Publisher
Springer Japan
Item Width
6.1in
Item Weight
185.8 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 Ito'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.

Product Identifiers

Publisher
Springer Japan
ISBN-10
4431551220
ISBN-13
9784431551225
eBay Product ID (ePID)
201645467

Product Key Features

Author
Makiko Nisio
Publication Name
Stochastic Control Theory : Dynamic Programming Principle
Format
Hardcover
Language
English
Publication Year
2014
Series
Probability Theory and Stochastic Modelling Ser.
Type
Textbook
Number of Pages
Xv, 250 Pages

Dimensions

Item Length
9.3in
Item Width
6.1in
Item Weight
185.8 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
Lccn
2014-953914
Dewey Decimal
003.76
Intended Audience
Scholarly & Professional
Dewey Edition
23
Illustrated
Yes
Genre
Mathematics

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