Stochastic Analysis, Filtering, and Stochastic Optimization
Stochastic Analysis, Filtering, and Stochastic Optimization

Author: George Yin

Publisher: Springer Nature

Published: 2022-04-22

Total Pages: 466

ISBN-13: 3030985199

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This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.

Stochastic Analysis, Control, Optimization and Applications
Stochastic Analysis, Control, Optimization and Applications

Author: William M. McEneaney

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 660

ISBN-13: 1461217849

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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.

Fundamentals of Stochastic Filtering
Fundamentals of Stochastic Filtering

Author: Alan Bain

Publisher: Springer Science & Business Media

Published: 2008-10-08

Total Pages: 395

ISBN-13: 0387768963

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This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.

An Introduction to Stochastic Filtering Theory
An Introduction to Stochastic Filtering Theory

Author: Jie Xiong

Publisher: Oxford University Press

Published: 2008-04-17

Total Pages: 285

ISBN-13: 0199219702

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Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance.As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filteringmodels has yielded exciting results.In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.

Stochastic Analysis, Stochastic Systems, and Applications to Finance
Stochastic Analysis, Stochastic Systems, and Applications to Finance

Author: Allanus Hak-Man Tsoi

Publisher: World Scientific

Published: 2011

Total Pages: 274

ISBN-13: 9814355704

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This book introduces some advanced topics in probability theories ? both pure and applied ? is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling.

Applied Stochastic Analysis
Applied Stochastic Analysis

Author: Ioannis Karatzas

Publisher: Springer

Published: 1992

Total Pages: 332

ISBN-13:

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This volume contains papers presented during a four-day Workshop that took place at Rutgers University from 29 April to 2 May, 1991. The purpose of this workshop was to promote interaction among specialists in these areas byproviding for all an up-to-date picture of current issues and outstanding problems. The topics covered include singular stochasticcontrol, queuing networks, the mathematical theory of stochastic optimization and filtering, adaptive control and the estimation for random fields and its connections with simulated annealing, statistical mechanics, and combinatorial optimization.

Applied Stochastic Analysis
Applied Stochastic Analysis

Author: Ioannis Karatzas

Publisher: Springer

Published: 2014-03-12

Total Pages: 315

ISBN-13: 9783662213902

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This volume contains papers presented during a four-day Workshop that took place at Rutgers University from 29 April to 2 May, 1991. The purpose of this workshop was to promote interaction among specialists in these areas byproviding for all an up-to-date picture of current issues and outstanding problems. The topics covered include singular stochasticcontrol, queuing networks, the mathematical theory of stochastic optimization and filtering, adaptive control and the estimation for random fields and its connections with simulated annealing, statistical mechanics, and combinatorial optimization.

Optimal Filtering
Optimal Filtering

Author: V.N. Fomin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 387

ISBN-13: 9401153264

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This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to [27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems.

Stochastic Filtering with Applications in Finance
Stochastic Filtering with Applications in Finance

Author: Ramaprasad Bhar

Publisher: World Scientific

Published: 2010

Total Pages: 354

ISBN-13: 9814304859

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This book provides a comprehensive account of stochastic filtering as a modeling tool in finance and economics. It aims to present this very important tool with a view to making it more popular among researchers in the disciplines of finance and economics. It is not intended to give a complete mathematical treatment of different stochastic filtering approaches, but rather to describe them in simple terms and illustrate their application with real historical data for problems normally encountered in these disciplines. Beyond laying out the steps to be implemented, the steps are demonstrated in the context of different market segments. Although no prior knowledge in this area is required, the reader is expected to have knowledge of probability theory as well as a general mathematical aptitude. Its simple presentation of complex algorithms required to solve modeling problems in increasingly sophisticated financial markets makes this book particularly valuable as a reference for graduate students and researchers interested in the field. Furthermore, it analyses the model estimation results in the context of the market and contrasts these with contemporary research publications. It is also suitable for use as a text for graduate level courses on stochastic modeling.