Inequalities For Stochastic Processes And Problems Of Stochastic Control
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Inequalities For Stochastic Processes And Problems Of Stochastic Control
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Author : S. D. Jacka
language : en
Publisher:
Release Date : 1983
Inequalities For Stochastic Processes And Problems Of Stochastic Control written by S. D. Jacka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Stochastic Control Theory
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Author : Makiko Nisio
language : en
Publisher: Springer
Release Date : 2014-11-27
Stochastic Control Theory written by Makiko Nisio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.
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.
Applications Of Variational Inequalities In Stochastic Control
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Author : A. Bensoussan
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Applications Of Variational Inequalities In Stochastic Control written by A. Bensoussan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
Applications of Variational Inequalities in Stochastic Control
Stochastic Processes And Filtering Theory
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Author : Andrew H. Jazwinski
language : en
Publisher: Courier Corporation
Release Date : 2013-04-15
Stochastic Processes And Filtering Theory written by Andrew H. Jazwinski and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Science categories.
This unified treatment presents material previously available only in journals, and in terms accessible to engineering students. Although theory is emphasized, it discusses numerous practical applications as well. 1970 edition.
Applied Stochastic Control Of Jump Diffusions
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Author : Bernt Øksendal
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-26
Applied Stochastic Control Of Jump Diffusions written by Bernt Øksendal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.
Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Numerical Methods For Stochastic Control Problems In Continuous Time
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Author : Harold J. Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Numerical Methods For Stochastic Control Problems In Continuous Time written by Harold J. Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Language Arts & Disciplines categories.
The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.
Probability Theory And Stochastic Processes With Applications Second Edition
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Author : Oliver Knill
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-01-31
Probability Theory And Stochastic Processes With Applications Second Edition written by Oliver Knill and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-31 with Mathematics categories.
This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.
Control And System Theory Of Discrete Time Stochastic Systems
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Author : Jan H. van Schuppen
language : en
Publisher: Springer Nature
Release Date : 2021-08-02
Control And System Theory Of Discrete Time Stochastic Systems written by Jan H. van Schuppen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Technology & Engineering categories.
This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.
Optimal Stopping And Free Boundary Problems
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Author : Goran Peskir
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-10
Optimal Stopping And Free Boundary Problems written by Goran Peskir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-10 with Mathematics categories.
This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.
Issues In Statistics Decision Making And Stochastics 2013 Edition
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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2013-05-01
Issues In Statistics Decision Making And Stochastics 2013 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-01 with Mathematics categories.
Issues in Statistics, Decision Making, and Stochastics: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Regular and Chaotic Dynamics. The editors have built Issues in Statistics, Decision Making, and Stochastics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Regular and Chaotic Dynamics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Statistics, Decision Making, and Stochastics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.