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Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications Author X Mao
ISBN-10 9780857099402
Release 2007-12-30
Pages 440
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This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systems Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists



Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications Author Avner Friedman
ISBN-10 9781483217871
Release 2014-06-20
Pages 248
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Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.



Stochastic Differential Equations

Stochastic Differential Equations Author Bernt Øksendal
ISBN-10 9783642143946
Release 2010-11-09
Pages 379
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Stochastic Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Stochastic Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Stochastic Differential Equations book for free.



Stochastic Differential Equations and Their Applications

Stochastic Differential Equations and Their Applications Author Xuerong Mao
ISBN-10 1898563268
Release 1997-01-01
Pages 366
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Stochastic Differential Equations and Their Applications has been writing in one form or another for most of life. You can find so many inspiration from Stochastic Differential Equations and Their Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Stochastic Differential Equations and Their Applications book for free.



Stochastic Differential Equations

Stochastic Differential Equations Author K. Sobczyk
ISBN-10 9789401137126
Release 2013-12-01
Pages 400
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Stochastic Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Stochastic Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Stochastic Differential Equations book for free.



Stochastic Differential Equations

Stochastic Differential Equations Author Ludwig Arnold
ISBN-10 0486482367
Release 2013
Pages 256
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Practical and not too rigorous, this highly readable text on stochastic calculus provides an excellent introduction to stochastic partial differential equations. Written at a moderately advanced level, it covers important topics often ignored by other texts on the subject—including Fokker-Planck equations—and it functions as both a classroom text and a reference for professionals and students. The only prerequisite is the mathematical preparation usual for students of physical and engineering sciences. An introductory chapter, intended for reference and review, covers the basics of probability theory. Subsequent chapters focus on Markov and diffusion processes, Wiener process and white noise, and stochastic integrals and differential equations. Additional topics include questions of modeling and approximation, stability of stochastic dynamic systems, optimal filtering of a disturbed signal, and optimal control of stochastic dynamic systems.



Stochastic Differential Equations

Stochastic Differential Equations Author Peter H. Baxendale
ISBN-10 9789812706621
Release 2007
Pages 393
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The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.



Numerical Solution of Stochastic Differential Equations

Numerical Solution of Stochastic Differential Equations Author Peter E. Kloeden
ISBN-10 9783662126165
Release 2013-04-17
Pages 636
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The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP



Theory of Stochastic Differential Equations with Jumps and Applications

Theory of Stochastic Differential Equations with Jumps and Applications Author Rong SITU
ISBN-10 9780387251752
Release 2006-05-06
Pages 434
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Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.



Forward Backward Stochastic Differential Equations and their Applications

Forward Backward Stochastic Differential Equations and their Applications Author Jin Ma
ISBN-10 9783540488316
Release 2007-04-24
Pages 278
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This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.



Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential Equations with Applications Author Kai Liu
ISBN-10 1420034820
Release 2005-08-23
Pages 312
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Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings. This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics. In recent years, this area of study has become the focus of increasing attention, and the relevant literature has expanded greatly. Stability of Infinite Dimensional Stochastic Differential Equations with Applications makes up-to-date material in this important field accessible even to newcomers and lays the foundation for future advances.



Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications Author Łukasz Delong
ISBN-10 9781447153313
Release 2013-06-12
Pages 288
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Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.



Simulation and Inference for Stochastic Differential Equations

Simulation and Inference for Stochastic Differential Equations Author Stefano M. Iacus
ISBN-10 0387758399
Release 2009-04-27
Pages 286
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This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.



Modeling with It Stochastic Differential Equations

Modeling with It   Stochastic Differential Equations Author E. Allen
ISBN-10 9781402059537
Release 2007-03-08
Pages 230
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This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.



Stochastic Differential Equations

Stochastic Differential Equations Author Michael J. Panik
ISBN-10 9781119377405
Release 2017-03-15
Pages 304
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A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.



An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations Author Lawrence C. Evans
ISBN-10 9781470410544
Release 2012-12-11
Pages 151
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These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).



Stochastic Differential Equations in Infinite Dimensions

Stochastic Differential Equations in Infinite Dimensions Author Leszek Gawarecki
ISBN-10 9783642161940
Release 2010-11-29
Pages 291
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The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.