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Ergodic Control Of Diffusion Processes
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Book Synopsis Ergodic Control of Diffusion Processes by : Ari Arapostathis
Download or read book Ergodic Control of Diffusion Processes written by Ari Arapostathis and published by Cambridge University Press. This book was released on 2012 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.
Book Synopsis Ergodicity for Infinite Dimensional Systems by : Giuseppe Da Prato
Download or read book Ergodicity for Infinite Dimensional Systems written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 1996-05-16 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book on stochastic modelling of infinite dimensional dynamical systems.
Book Synopsis Diffusion Processes and their Sample Paths by : Kiyosi Itô
Download or read book Diffusion Processes and their Sample Paths written by Kiyosi Itô and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
Book Synopsis Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems by : Xi-Ren Cao
Download or read book Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems written by Xi-Ren Cao and published by Springer Nature. This book was released on 2020-05-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.
Book Synopsis Adaptive Control, Filtering, and Signal Processing by : K.J. Aström
Download or read book Adaptive Control, Filtering, and Signal Processing written by K.J. Aström and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of adaptive systems, which encompasses recursive identification, adaptive control, filtering, and signal processing, has been one of the most active areas of the past decade. Since adaptive controllers are fundamentally nonlinear controllers which are applied to nominally linear, possibly stochastic and time-varying systems, their theoretical analysis is usually very difficult. Nevertheless, over the past decade much fundamental progress has been made on some key questions concerning their stability, convergence, performance, and robustness. Moreover, adaptive controllers have been successfully employed in numerous practical applications, and have even entered the marketplace.
Book Synopsis Kolmogorov Operators and Their Applications by : Stéphane Menozzi
Download or read book Kolmogorov Operators and Their Applications written by Stéphane Menozzi and published by Springer Nature. This book was released on with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modern Trends in Controlled Stochastic Processes by : Alexey B. Piunovskiy
Download or read book Modern Trends in Controlled Stochastic Processes written by Alexey B. Piunovskiy and published by Luniver Press. This book was released on 2010-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: World leading experts give their accounts of the modern mathematical models in the field: Markov Decision Processes, controlled diffusions, piece-wise deterministic processes etc, with a wide range of performance functionals. One of the aims is to give a general view on the state-of-the-art. The authors use Dynamic Programming, Convex Analytic Approach, several numerical methods, index-based approach and so on. Most chapters either contain well developed examples, or are entirely devoted to the application of the mathematical control theory to real life problems from such fields as Insurance, Portfolio Optimization and Information Transmission. The book will enable researchers, academics and research students to get a sense of novel results, concepts, models, methods, and applications of controlled stochastic processes.
Book Synopsis Stochastic Theory and Control by : Bozenna Pasik-Duncan
Download or read book Stochastic Theory and Control written by Bozenna Pasik-Duncan and published by Springer. This book was released on 2003-07-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains almost all of the papers that were presented at the Workshop on Stochastic Theory and Control that was held at the Univ- sity of Kansas, 18–20 October 2001. This three-day event gathered a group of leading scholars in the ?eld of stochastic theory and control to discuss leading-edge topics of stochastic control, which include risk sensitive control, adaptive control, mathematics of ?nance, estimation, identi?cation, optimal control, nonlinear ?ltering, stochastic di?erential equations, stochastic p- tial di?erential equations, and stochastic theory and its applications. The workshop provided an opportunity for many stochastic control researchers to network and discuss cutting-edge technologies and applications, teaching and future directions of stochastic control. Furthermore, the workshop focused on promoting control theory, in particular stochastic control, and it promoted collaborative initiatives in stochastic theory and control and stochastic c- trol education. The lecture on “Adaptation of Real-Time Seizure Detection Algorithm” was videotaped by the PBS. Participants of the workshop have been involved in contributing to the documentary being ?lmed by PBS which highlights the extraordinary work on “Math, Medicine and the Mind: Discovering Tre- ments for Epilepsy” that examines the e?orts of the multidisciplinary team on which several of the participants of the workshop have been working for many years to solve one of the world’s most dramatic neurological conditions. Invited high school teachers of Math and Science were among the part- ipants of this professional meeting.
Book Synopsis Directions in Mathematical Systems Theory and Optimization by : Anders Rantzer
Download or read book Directions in Mathematical Systems Theory and Optimization written by Anders Rantzer and published by Springer. This book was released on 2003-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, his recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.
Author :Daniel Hernández-Hernández Publisher :Springer Science & Business Media ISBN 13 :0817683372 Total Pages :331 pages Book Rating :4.8/5 (176 download)
Book Synopsis Optimization, Control, and Applications of Stochastic Systems by : Daniel Hernández-Hernández
Download or read book Optimization, Control, and Applications of Stochastic Systems written by Daniel Hernández-Hernández and published by Springer Science & Business Media. This book was released on 2012-08-15 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.
Book Synopsis Markov Processes and Controlled Markov Chains by : Zhenting Hou
Download or read book Markov Processes and Controlled Markov Chains written by Zhenting Hou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.
Book Synopsis Probabilistic Theory of Mean Field Games with Applications I by : René Carmona
Download or read book Probabilistic Theory of Mean Field Games with Applications I written by René Carmona and published by Springer. This book was released on 2018-03-01 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Book Synopsis Probabilistic Theory of Mean Field Games with Applications II by : René Carmona
Download or read book Probabilistic Theory of Mean Field Games with Applications II written by René Carmona and published by Springer. This book was released on 2018-03-08 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis
Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Book Synopsis Selected Topics on Continuous-time Controlled Markov Chains and Markov Games by : Tomas Prieto-Rumeau
Download or read book Selected Topics on Continuous-time Controlled Markov Chains and Markov Games written by Tomas Prieto-Rumeau and published by World Scientific. This book was released on 2012 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas. An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown. This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.
Book Synopsis Stochastic Analysis, Control, Optimization and Applications by : William M. McEneaney
Download or read book Stochastic Analysis, Control, Optimization and Applications written by William M. McEneaney and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.
Book Synopsis Numerical Methods for Stochastic Control Problems in Continuous Time by : Harold Kushner
Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
