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Stochastic Differential Equations: An Introduction with Applications (Universitext) download epub

by Bernt Øksendal

Epub Book: 1840 kb. | Fb2 Book: 1405 kb.

This book gives an introduction to the basic theory of stochastic calculus and its applications.

This book gives an introduction to the basic theory of stochastic calculus and its applications. economics, biology and physics.

Stochastic Dierential Equations

Stochastic Dierential Equations. Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest. To My Family Eva, Elise, Anders and Karina. Some new exercises have been added. Moreover, to facilitate the use of the book each chapter has been divided into subsections.

An Introduction with Applications. Authors: Øksendal, Bernt. The book is a first choice for courses at graduate level in applied stochastic differential equations. Evelyn Buckwar, Zentralblatt MATH, Vol. 1025, 2003).

PDF On Jan 1, 2000, Bernt Oksendal and others published Stochastic Differential Equations: An Introduction with . This book uses continuous time stochastic calculus as a mathematical tool for financial modeling.

This book uses continuous time stochastic calculus as a mathematical tool for financial modeling. In this appendix we plan to give a quick (informal) introduction to stochastic differential equations (SDEs) for the reader who is not familiar with this field. These notes are far from being complete or fully rigorous, in that we privilege the intuitive aspect, but we give references for the reader.

I thank them all for helping to improve the book. My thanks also go to Dina Haraldsson, who once again has performed the typing and drawn the ?gures with great skill.

Ships from and sold by Cherry Books. 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. My thanks also go to Dina Haraldsson, who once again has performed the typing and drawn the figures with great skill. 1. Introduction To convince the reader that stochastic differential equations are an important subject let us mention some situations where such equations appear and can be used: . Stochastic Analogs of Classical Differential Equations If we allow for some randomness in some of the coefficients of a differential equation we often obtain a more realistic mathematical model of the situation.

Bernt Øksendal (auth. These notes are an attempt to approach the subject from the nonexpert point of view. Not knowing anything.

Stochastic Differential Equations. Diffusions: Basic Properties. oceedings{cDE, title {Stochastic Differential Equations: An Introduction with Applications}, author {Bernt {O}ksendal}, year {1985} }. Bernt Øksendal. Other Topics in Diffusion Theory. Applications to Boundary Value Problems. Application to Optimal Stopping. Application to Stochastic Control. Application to Mathematical Finance. Some Mathematical Preliminaries. The Ito Formula and the Martingale Representation Theorem. Stochastic Differential Equations.

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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.

Comments: (7)

This book should have a list of prerequisites that one should read and ingrain into their minds before attempting to read this book... I can see this being helpful for a full time graduate student or someone that is consistently exposed to ODE/PDEs and measure theory, but I was assigned this book for a part-time graduate degree program (which is geared towards working professionals) and I found the terseness and assumptions placed on the reader to be a real detriment to learning the material... You constantly have to flip through pages to refer to previous equations, or go to the appendix to decipher syntax that I have never encountered in my other graduate level math classes, that it made it very hard to see what the point of most of the equations were trying to accomplish...

My previous degrees were in engineering, so will admit that I do not have the natural 'math' mind... But I do feel that some examples on each topic would have helped cement their importance.... Instead you are constantly thrust into a slightly new topic, without much explanation its distinction... I felt you were required to take photocopies of pages and inspect each minutia of every new equation to actually understand what new insight it brought to analysis....
This book is offers an excellent introduction to SDE but limiting the text to integration w.r.t Brownian motion.

The book is structured by first introducing 6 problems which are solved using the concepts and theory discussed in the chapters that follow. This is an excellent pedagogical tool, that is used to focus the mind on applications, in order to understand the abstract concepts discussed.

The level of mathematics is moderate in difficulty with some proofs omitted (but with references included) for the sake of not veering away too far from the main concepts (and the need to introduce further preliminaries to understand the proof).

There are also exercises included (with some solutions and hints) that allows the reader to solidify the understanding and applications.

The follow-up text is commonly the Karatzas and Shreve book,though its level of difficulty is substantially higher than this text.
From the cover, one can infer that this book means business. Some books still try to be artistic to attract audiences, whereas this book does away with a creative cover altogether. How often do you see that a book's cover contains five sample paths of a geometric Brownian Motion? Inside, Oksendal writes very clearly and uses the same format throughout. Although the topic is not the easiest to understand, you can acquire the skills that would allow you to gain sufficient knowledge of stochastic differential equations. He starts off with a good introduction and then moves on to the main topics. His applications to finance are also very useful for those in the field. A word of caution is that you would need a decent background in mathematics to read this book, but it is easier than Shreve or Karatzas and Shreve.
Misleading title - NOT AN INTRODUCTION. There are much better places to start with stochastic integration.
If you aren't a bit of a Math wonk, this book can be a bit daunting. But it is worth wading through the Math if you want to understand the "WHY" behind all those formulas and results. If you are looking for a gentler introduction and the "real formulas" Quants use, check out Paul Wilmott's books.

The text generally starts with an intuitive example for the chapter and then starts methodically working through the underlying mathematics to get to the meaty results. The exercises are worth the effort as they reinforce the chapter work and offer additional insights.
Oksendal suffers from measurement theory minuatae in order to make this a rigourous text. Frustatingly the author has economised in proofs, leaving out the 'unnecessary' intermediate steps etc wasting a lot of your time to reconstruct. If you've never seen an SDE before, read Elementary Stochastic Equations by Miksovich before attempting this 'Introduction' - really an intermediate text. I really didn't like this book, more could be done to make it comprehensible with less reader effort.
The title says it all. It is an excellent book for beginners to get in to stochastic calculus. A small suggestion that you revise your ODE before you tackle this book as it will ease the references the author likes to make to ODE.
The book makes us understand the actual importance of the probability.
Today the books about the stochastic equations have superated the interest of the traditional analysis.
The author explicates with competence the definition of the martingale, filter or Markov chain. The applications are about the finance, the control theory, the problem of stopping.
Stochastic Differential Equations: An Introduction with Applications (Universitext) download epub
Author: Bernt Øksendal
ISBN: 3540047581
Category: Science & Math
Subcategory: Mathematics
Language: English
Publisher: Springer; 6th edition (March 4, 2014)
Pages: 379 pages