Stochastic Differential Equations and Applications Book

Stochastic Differential Equations and Applications


  • Author : Avner Friedman
  • Publisher : Academic Press
  • Release Date : 2014-06-20
  • Genre: Mathematics
  • Pages : 248
  • ISBN 10 : 9781483217871

DOWNLOAD BOOK
Stochastic Differential Equations and Applications Excerpt :

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 and Applications Book

Stochastic Differential Equations and Applications


  • Author : X Mao
  • Publisher : Elsevier
  • Release Date : 2007-12-30
  • Genre: Mathematics
  • Pages : 440
  • ISBN 10 : 9780857099402

DOWNLOAD BOOK
Stochastic Differential Equations and Applications Excerpt :

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 Book

Stochastic Differential Equations


  • Author : Bernt Oksendal
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Mathematics
  • Pages : 188
  • ISBN 10 : 9783662025741

DOWNLOAD BOOK
Stochastic Differential Equations Excerpt :

From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2

Theory of Stochastic Differential Equations with Jumps and Applications Book

Theory of Stochastic Differential Equations with Jumps and Applications


  • Author : Rong SITU
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-05-06
  • Genre: Technology & Engineering
  • Pages : 434
  • ISBN 10 : 9780387251752

DOWNLOAD BOOK
Theory of Stochastic Differential Equations with Jumps and Applications Excerpt :

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.

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance Book

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance


  • Author : Carlos A. Braumann
  • Publisher : John Wiley & Sons
  • Release Date : 2019-03-08
  • Genre: Mathematics
  • Pages : 304
  • ISBN 10 : 9781119166078

DOWNLOAD BOOK
Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance Excerpt :

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of applicatio

Forward Backward Stochastic Differential Equations and their Applications Book

Forward Backward Stochastic Differential Equations and their Applications


  • Author : Jin Ma
  • Publisher : Springer
  • Release Date : 2007-04-24
  • Genre: Mathematics
  • Pages : 278
  • ISBN 10 : 9783540488316

DOWNLOAD BOOK
Forward Backward Stochastic Differential Equations and their Applications Excerpt :

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.

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

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


  • Author : Łukasz Delong
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-12
  • Genre: Mathematics
  • Pages : 288
  • ISBN 10 : 9781447153313

DOWNLOAD BOOK
Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications Excerpt :

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.

Stochastic Differential Equations in Infinite Dimensions Book

Stochastic Differential Equations in Infinite Dimensions


  • Author : Leszek Gawarecki
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-11-29
  • Genre: Mathematics
  • Pages : 291
  • ISBN 10 : 9783642161940

DOWNLOAD BOOK
Stochastic Differential Equations in Infinite Dimensions Excerpt :

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.

Applied Stochastic Differential Equations Book

Applied Stochastic Differential Equations


  • Author : Simo Särkkä
  • Publisher : Cambridge University Press
  • Release Date : 2019-05-02
  • Genre: Business & Economics
  • Pages : 327
  • ISBN 10 : 9781316510087

DOWNLOAD BOOK
Applied Stochastic Differential Equations Excerpt :

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Numerical Solution of Stochastic Differential Equations Book

Numerical Solution of Stochastic Differential Equations


  • Author : Peter E. Kloeden
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Mathematics
  • Pages : 636
  • ISBN 10 : 9783662126165

DOWNLOAD BOOK
Numerical Solution of Stochastic Differential Equations Excerpt :

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

An Introduction to Stochastic Differential Equations Book

An Introduction to Stochastic Differential Equations


  • Author : Lawrence C. Evans
  • Publisher : American Mathematical Soc.
  • Release Date : 2012-12-11
  • Genre: Mathematics
  • Pages : 151
  • ISBN 10 : 9781470410544

DOWNLOAD BOOK
An Introduction to Stochastic Differential Equations Excerpt :

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 mat

Stability of Infinite Dimensional Stochastic Differential Equations with Applications Book

Stability of Infinite Dimensional Stochastic Differential Equations with Applications


  • Author : Kai Liu
  • Publisher : Chapman and Hall/CRC
  • Release Date : 2005-08-23
  • Genre: Mathematics
  • Pages : 312
  • ISBN 10 : 158488598X

DOWNLOAD BOOK
Stability of Infinite Dimensional Stochastic Differential Equations with Applications Excerpt :

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.

Modeling with It   Stochastic Differential Equations Book

Modeling with It Stochastic Differential Equations


  • Author : E. Allen
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-03-08
  • Genre: Mathematics
  • Pages : 230
  • ISBN 10 : 9781402059537

DOWNLOAD BOOK
Modeling with It Stochastic Differential Equations Excerpt :

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.