Probability with Martingales PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Probability with Martingales PDF full book. Access full book title Probability with Martingales by David Williams. Download full books in PDF and EPUB format.
Author: David Williams
Publisher: Cambridge University Press
ISBN: 9780521406055
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
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: David Williams
Publisher: Cambridge University Press
ISBN: 9780521406055
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
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: Daniel Revuz
Publisher: Springer Science & Business Media
ISBN: 3662064006
Category : Mathematics
Languages : en
Pages : 608
Get Book Here
Book Description
"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." –BULLETIN OF THE L.M.S.
Author: P. Hall
Publisher: Academic Press
ISBN: 1483263223
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Author: Francis Hirsch
Publisher: Springer Science & Business Media
ISBN: 8847019087
Category : Mathematics
Languages : en
Pages : 412
Get Book Here
Book Description
We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings. They are developed in eight chapters, with about a hundred of exercises.
Author: Norihiko Kazamaki
Publisher: Springer
ISBN: 3540484213
Category : Mathematics
Languages : en
Pages : 102
Get Book Here
Book Description
In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.
Author: Richard Durrett
Publisher: Wadsworth Publishing Company
ISBN: 9780534030650
Category : Mathematics
Languages : en
Pages : 328
Get Book Here
Book Description
Author: Jean-François Le Gall
Publisher: Springer
ISBN: 3319310895
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
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: Marek Musiela
Publisher: Springer Science & Business Media
ISBN: 3662221322
Category : Mathematics
Languages : en
Pages : 521
Get Book Here
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: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521775939
Category : Mathematics
Languages : en
Pages : 498
Get Book Here
Book Description
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.
Author: Paul F. X. Müller
Publisher: Cambridge University Press
ISBN: 1108838677
Category : Mathematics
Languages : en
Pages : 517
Get Book Here
Book Description
This book presents the probabilistic methods around Hardy martingales for applications to complex, harmonic, and functional analysis.
