Diffusions, Markov Processes, and Martingales: Volume 1, Foundations PDF Download

Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521775946
Category : Mathematics
Languages : en
Pages : 412

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Book Description
Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 1107717493
Category : Mathematics
Languages : en
Pages : 412

View

Book Description
Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

Author: David Williams
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description

Author: David Williams
Publisher: Cambridge University Press
ISBN: 9780521406055
Category : Mathematics
Languages : en
Pages : 274

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Book Description
This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.

Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521775939
Category : Mathematics
Languages : en
Pages : 498

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Book Description
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.

Author: Jean-François Le Gall
Publisher: Springer
ISBN: 3319310895
Category : Mathematics
Languages : en
Pages : 282

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Book Description
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Author: W. V. D. Hodge
Publisher: Cambridge University Press
ISBN: 0521469015
Category : Mathematics
Languages : en
Pages : 408

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Book Description
All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Author: Olav Kallenberg
Publisher: Springer Science & Business Media
ISBN: 9780387953137
Category : Mathematics
Languages : en
Pages : 670

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Book Description
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Author: Marek Musiela
Publisher: Springer Science & Business Media
ISBN: 3662221322
Category : Mathematics
Languages : en
Pages : 521

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Book Description
A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.

Author: Ioannis Karatzas
Publisher: Springer
ISBN: 1461209498
Category : Mathematics
Languages : en
Pages : 490

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Book Description
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.