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Book
Hybrid switching diffusions : properties and applications
Authors: ---
ISBN: 1441911049 9786612835131 1441911057 1282835130 Year: 2010 Publisher: New York : Springer,

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Abstract

This book presents a comprehensive study of hybrid switching diffusion processes and their applications. The motivations for studying such processes originate from emerging and existing applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, financial engineering, and modeling, analysis, and control and optimization of large-scale systems, under the influence of random environment. One of the distinct features of the processes under consideration is the coexistence of continuous dynamics and discrete events. This book is written for applied mathematicians, applied probabilists, systems engineers, control scientists, operations researchers, and financial analysts. Selected materials from the book may also be used in a graduate level course on stochastic processes and applications or a course on hybrid systems. A large part of the book is concerned with the discrete event process depending on the continuous dynamics. In addition to the existence and uniqueness of solutions of switching diffusion equations, regularity, Feller and strong Feller properties, continuous and smooth dependence on initial data, recurrence, ergodicity, invariant measures, and stability are dealt with. Numerical methods for solutions of switching diffusions are developed; algorithms for approximation to invariant measures are investigated. Two-time-scale models are also examined. The results presented in the book are useful to researchers and practitioners who need to use stochastic models to deal with hybrid stochastic systems, and to treat real-world problems when continuous dynamics and discrete events are intertwined, in which the traditional approach using stochastic differential equations alone is no longer adequate.

Keywords

Hybrid systems. --- Mathematics. --- Stochastic processes -- Mathematical models. --- Stochastic processes --- Hybrid systems --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical models --- Diffusion processes. --- Stochastic differential equations. --- Switching theory. --- Operations research. --- Decision making. --- Probabilities. --- Control engineering. --- Robotics. --- Mechatronics. --- Automation. --- Probability Theory and Stochastic Processes. --- Operation Research/Decision Theory. --- Robotics and Automation. --- Control, Robotics, Mechatronics. --- Automatic control --- Digital electronics --- Electric networks --- Electric switchgear --- Information theory --- Logic, Symbolic and mathematical --- Machine theory --- Mathematical physics --- System analysis --- Telecommunication --- Differential equations --- Fokker-Planck equation --- Markov processes --- Distribution (Probability theory. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Automatic factories --- Automatic production --- Computer control --- Engineering cybernetics --- Factories --- Mechanization --- Assembly-line methods --- Automatic machinery --- CAD/CAM systems --- Robotics --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Decision making


Book
Stochastic optimal control and the U.S. financial debt crisis
Author:
ISBN: 1489986316 146143078X 9786613698032 1461430798 1280787643 Year: 2012 Publisher: New York : Springer,

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Abstract

Stochastic Optimal Control (SOC)—a mathematical theory concerned with minimizing a cost (or maximizing a payout) pertaining to a controlled dynamic process under uncertainty—has proven incredibly helpful to understanding and predicting debt crises and evaluating proposed financial regulation and risk management. Stochastic Optimal Control and the U.S. Financial Debt Crisis analyzes SOC in relation to the 2008 U.S. financial crisis, and offers a detailed framework depicting why such a methodology is best suited for reducing financial risk and addressing key regulatory issues.  Topics discussed include the inadequacies of the current approaches underlying financial regulations, the use of SOC to explain debt crises and superiority over existing approaches to regulation, and the domestic and international applications of SOC to financial crises.  Principles in this book will appeal to economists, mathematicians, and researchers interested in the U.S. financial debt crisis and optimal risk management. Jerome L. Stein has been an emeritus professor of economics at Brown University since 1993, and has served as a visiting professor of applied mathematics since 1997. He is the author of nine research monographs, and has published over 100 journal articles in such leading publications as American Economic Review, Review of Economics and Statistics, Journal of Banking and Finance, and Contemporary Mathematics. He has served on the editorial boards of the Journal of Finance, American Economic Review, Journal of International and Comparative Economics, and the Journal of Banking and Finance.

Keywords

Debts, Public -- Mathematical models. --- Endogenous growth (Economics) -- Mathematical models. --- Equilibrium (Economics) -- Mathematical models. --- Stochastic processes -- Mathematical models. --- Debt --- Stochastic processes --- Finance --- Business & Economics --- Banking --- Finance - General --- Financial Management & Planning --- Investment & Speculation --- Mathematical models --- Debts, Public --- Stochastic control theory. --- Global Financial Crisis, 2008-2009. --- Global Economic Crisis, 2008-2009 --- Subprime Mortgage Crisis, 2008-2009 --- Finance. --- Probabilities. --- Statistics. --- Finance, general. --- Probability Theory and Stochastic Processes. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Financial crises --- Control theory --- Distribution (Probability theory. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- Currency question --- Statistics . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- United States --- United States. --- Economic conditions --- Mathematical models. --- AB --- ABSh --- Ameerika Ühendriigid --- America (Republic) --- Amerika Birlăshmish Shtatlary --- Amerika Birlăşmi Ştatları --- Amerika Birlăşmiş Ştatları --- Amerika ka Kelenyalen Jamanaw --- Amerika Qūrama Shtattary --- Amerika Qŭshma Shtatlari --- Amerika Qushma Shtattary --- Amerika (Republic) --- Amerikai Egyesült Államok --- Amerikanʹ Veĭtʹsėndi͡avks Shtattn --- Amerikări Pĕrleshu̇llĕ Shtatsem --- Amerikas Forenede Stater --- Amerikayi Miatsʻyal Nahangner --- Ameriketako Estatu Batuak --- Amirika Carékat --- AQSh --- Ar. ha-B. --- Arhab --- Artsot ha-Berit --- Artzois Ha'bris --- Bí-kok --- Ē.P.A. --- EE.UU. --- Egyesült Államok --- ĒPA --- Estados Unidos --- Estados Unidos da América do Norte --- Estados Unidos de América --- Estaos Xuníos --- Estaos Xuníos d'América --- Estatos Unitos --- Estatos Unitos d'America --- Estats Units d'Amèrica --- Ètats-Unis d'Amèrica --- États-Unis d'Amérique --- Fareyniḳṭe Shṭaṭn --- Feriene Steaten --- Feriene Steaten fan Amearika --- Forente stater --- FS --- Hēnomenai Politeiai Amerikēs --- Hēnōmenes Politeies tēs Amerikēs --- Hiwsisayin Amerikayi Miatsʻeal Tērutʻiwnkʻ --- Istadus Unidus --- Jungtinės Amerikos valstybės --- Mei guo --- Mei-kuo --- Meiguo --- Mî-koet --- Miatsʻyal Nahangner --- Miguk --- Na Stàitean Aonaichte --- NSA --- S.U.A. --- SAD --- Saharat ʻAmērik --- SASht --- Severo-Amerikanskie Shtaty --- Severo-Amerikanskie Soedinennye Shtaty --- Si͡evero-Amerikanskīe Soedinennye Shtaty --- Sjedinjene Američke Države --- Soedinennye Shtaty Ameriki --- Soedinennye Shtaty Severnoĭ Ameriki --- Soedinennye Shtaty Si͡evernoĭ Ameriki --- Spojené obce severoamerick --- Spojené staty americk --- SShA --- Stadoù-Unanet Amerika --- Stáit Aontaithe Mheirice --- Stany Zjednoczone --- Stati Uniti --- Stati Uniti d'America --- Stâts Unîts --- Stâts Unîts di Americhe --- Steatyn Unnaneysit --- Steatyn Unnaneysit America --- SUA --- Sŭedineni amerikanski shtati --- Sŭedinenite shtati --- Tetã peteĩ reko Amérikagua --- U.S. --- U.S.A. --- United States of America --- Unol Daleithiau --- Unol Daleithiau America --- Unuiĝintaj Ŝtatoj de Ameriko --- US --- USA --- Usono --- Vaeinigte Staatn --- Vaeinigte Staatn vo Amerika --- Vereinigte Staaten --- Vereinigte Staaten von Amerika --- Verenigde State van Amerika --- Verenigde Staten --- VS --- VSA --- Wááshindoon Bikéyah Ałhidadiidzooígí --- Wilāyāt al-Muttaḥidah --- Wilāyāt al-Muttaḥidah al-Amirīkīyah --- Wilāyāt al-Muttaḥidah al-Amrīkīyah --- Yhdysvallat --- Yunaeted Stet --- Yunaeted Stet blong Amerika --- ZDA --- Združene države Amerike --- Zʹi͡ednani Derz͡havy Ameryky --- Zjadnośone staty Ameriki --- Zluchanyi͡a Shtaty Ameryki --- Zlucheni Derz͡havy --- ZSA --- ABŞ --- Amerikanʹ Veĭtʹsėndi͡avks Shtattnė --- É.-U. --- ÉU --- Saharat ʻAmērikā --- Spojené obce severoamerické --- Spojené staty americké --- Stáit Aontaithe Mheiriceá --- Wááshindoon Bikéyah Ałhidadiidzooígíí

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