Author: F. Levieux
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
The definition and main properties of the stochastics integrals are examined. The differences between the solutions proposed by K. Ito and R.L. Stratonovitch are exposed. The question of the representation of diffusion processes by stochastic differential equations is examined in view of definition of a non-linear state variable representation of diffusion processes. (Author).
Equations Differentielles Stochastiques Au Sens de Stratonovitch Et de Ito (Stochastic Differential Equations in the Sense of Stratonovitch and of Ito).
Author: F. Levieux
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
The definition and main properties of the stochastics integrals are examined. The differences between the solutions proposed by K. Ito and R.L. Stratonovitch are exposed. The question of the representation of diffusion processes by stochastic differential equations is examined in view of definition of a non-linear state variable representation of diffusion processes. (Author).
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
The definition and main properties of the stochastics integrals are examined. The differences between the solutions proposed by K. Ito and R.L. Stratonovitch are exposed. The question of the representation of diffusion processes by stochastic differential equations is examined in view of definition of a non-linear state variable representation of diffusion processes. (Author).
Stochastic Differential Equations In Science And Engineering (With Cd-rom)
Author: Douglas Henderson
Publisher: World Scientific
ISBN: 9814480533
Category : Science
Languages : en
Pages : 240
Book Description
Traditionally, non-quantum physics has been concerned with deterministic equations where the dynamics of the system are completely determined by initial conditions. A century ago the discovery of Brownian motion showed that nature need not be deterministic. However, it is only recently that there has been broad interest in nondeterministic and even chaotic systems, not only in physics but in ecology and economics. On a short term basis, the stock market is nondeterministic and often chaotic. Despite its significance, there are few books available that introduce the reader to modern ideas in stochastic systems. This book provides an introduction to this increasingly important field and includes a number of interesting applications.
Publisher: World Scientific
ISBN: 9814480533
Category : Science
Languages : en
Pages : 240
Book Description
Traditionally, non-quantum physics has been concerned with deterministic equations where the dynamics of the system are completely determined by initial conditions. A century ago the discovery of Brownian motion showed that nature need not be deterministic. However, it is only recently that there has been broad interest in nondeterministic and even chaotic systems, not only in physics but in ecology and economics. On a short term basis, the stock market is nondeterministic and often chaotic. Despite its significance, there are few books available that introduce the reader to modern ideas in stochastic systems. This book provides an introduction to this increasingly important field and includes a number of interesting applications.
Government Reports Announcements
Author:
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 948
Book Description
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 948
Book Description
Government Reports Announcements & Index
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 956
Book Description
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 956
Book Description
Stochastic Differential Equations
Author: Bernt Oksendal
Publisher: Springer Science & Business Media
ISBN: 3662130505
Category : Mathematics
Languages : en
Pages : 218
Book Description
These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.
Publisher: Springer Science & Business Media
ISBN: 3662130505
Category : Mathematics
Languages : en
Pages : 218
Book Description
These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.
Bibliography of Scientific and Industrial Reports
Author:
Publisher:
ISBN:
Category : Technology
Languages : en
Pages : 658
Book Description
Publisher:
ISBN:
Category : Technology
Languages : en
Pages : 658
Book Description
On Stochastic Differential Equations
Author: Kiyosi Itô
Publisher: American Mathematical Soc.
ISBN: 0821812041
Category : Differential equations
Languages : en
Pages : 56
Book Description
Publisher: American Mathematical Soc.
ISBN: 0821812041
Category : Differential equations
Languages : en
Pages : 56
Book Description
An Introduction to Stochastic Differential Equations
Author: Lawrence C. Evans
Publisher: American Mathematical Soc.
ISBN: 1470410540
Category : Mathematics
Languages : en
Pages : 161
Book Description
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).
Publisher: American Mathematical Soc.
ISBN: 1470410540
Category : Mathematics
Languages : en
Pages : 161
Book Description
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).
On Stochastic Differential Equations in the Ito and in the Stratonovich Sense
Author: Brett Williams
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Stochastic Differential Equations
Author: Bernt Øksendal
Publisher: Springer Science & Business Media
ISBN: 3642143946
Category : Mathematics
Languages : en
Pages : 403
Book Description
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. This corrected 6th printing of the 6th edition contains additional corrections and useful improvements, based in part on helpful comments from the readers.
Publisher: Springer Science & Business Media
ISBN: 3642143946
Category : Mathematics
Languages : en
Pages : 403
Book Description
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. This corrected 6th printing of the 6th edition contains additional corrections and useful improvements, based in part on helpful comments from the readers.