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Author: Jean-François Le Gall
Publisher:
ISBN:
Category :
Languages : fr
Pages : 180
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Book Description
ON PRESENTE QUELQUES APPLICATIONS DE LA NOTION DE TEMPS LOCAL A LA THEORIE DES EQUATIONS DIFFERENTIELLES STOCHASTIQUES UNIDIMENSIONNELLES
Author: Jean-François Le Gall
Publisher:
ISBN:
Category :
Languages : fr
Pages : 180
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Book Description
ON PRESENTE QUELQUES APPLICATIONS DE LA NOTION DE TEMPS LOCAL A LA THEORIE DES EQUATIONS DIFFERENTIELLES STOCHASTIQUES UNIDIMENSIONNELLES
Author: Youssef Ouknine
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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: Daniel Revuz
Publisher: Springer Science & Business Media
ISBN: 3662217260
Category : Mathematics
Languages : en
Pages : 544
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Book Description
This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).
Author: Mohammed Mellouk
Publisher:
ISBN:
Category :
Languages : en
Pages : 124
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Book Description
LA THESE SE DECOMPOSE EN QUATRES PARTIES INDEPENDANTES QUI TRAITENT DE QUESTIONS RELATIVES AUX PROPRIETES DES TRAJECTOIRES DE DIFFUSIONS (THEOREME DE SUPPORT, GRANDES DEVIATIONS, LOI DE STRASSEN) ET DU TEMPS LOCAL BROWNIEN DANS DES SOUS ESPACES DE FONCTIONS CONTINUES MUNIS D'UNE TOPLOGIE PLUS FORTE QUE CELLE DEFINIE PAR LA NORME UNIFORME CLASSIQUE. PLUS PARTICULIEREMENT, CE TRAVAIL ANALYSE CES PROPRIETES DANS LES ESPACES DE BESOV-ORLICZ QUI CONSTITUENT LA CLASSE LA PLUS FINE RENDANT COMPTE DES PROPRIETES DES TRAJECTOIRES BROWNIENNES AINSI QU'IL RESULTE DES TRAVAUX DE CIESIELSKI, KERKYACHARIAN ET ROYNETTE PAR L'INTERMEDIAIRE DES DESCRIPTIONS ANALYTIQUES DES ESPACES DE BESOV-ORLICZ SUR LA BASE DE HAAR. DANS LES QUATRES PARTIES DE CE TRAVAIL, ON ETUDIE SUCCESSIVEMENT, DANS CES ESPACES, LA REGULARITE DE LA TRAJECTOIRE SPATIALE DU TEMPS LOCAL BROWNIEN (ON MONTRE GRACE A UNE VERSION, DUE A BIANE ET YOR, DU THEOREME DE RAY, QUE LA REGULARITE EN ESPACE DU TEMPS LOCAL BROWNIEN EST LA MEME QUE CELLE DU BROWNIEN LUI MEME), LES GRANDES DEVIATIONS DES EQUATIONS DIFFERENTIELLES ANTICIPATIVES (AU SENS DE STRATONOVICH), LE THEOREME DE SUPPORT DE STROOCK-VARADHAN DE CES MEMES EQUATIONS (EN UTILISANT L'APPROCHE MILLET-SANZ QUI FAIT USAGE DE TRANSFORMATIONS ABSOLUMENT CONTINUES DE L'ESPACE DES TRAJECTOIRES CONSTRUITES PAR INTERPOLATION LINEAIRE ADAPTEE, ON CARACTERISE LE SUPPORT TOPLOGIQUE DE LA LOI DE CES EQUATIONS), LA QUATRIEME PARTIE, PLUS INDEPENDANTE QUE LES AUTRES, EST CONSACREE AU PRINCIPE DE GRANDES DEVIATIONS DES EQUATIONS D'EVOLUTIONS A COEFFICIENTS ALEATOIRES (CE RESULTAT EST OBTENU A L'AIDE D'UN PRINCIPE DE CONTRACTION ETENDU), GENERALISANT AINSI DIVERS TRAVAUX ANTERIEURS.
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.
Author: Andrei Borodin
Publisher: Birkhäuser
ISBN: 3034876521
Category : Mathematics
Languages : en
Pages : 478
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Book Description
There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.
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: Philip Protter
Publisher: Springer
ISBN: 3662100614
Category : Mathematics
Languages : en
Pages : 430
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Book Description
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
Author: Andrei N. Borodin
Publisher: Springer Science & Business Media
ISBN: 9783764367053
Category : Mathematics
Languages : en
Pages : 710
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Book Description
Here is easy reference to a wealth of facts and formulae associated with Brownian motion, collecting in one volume more than 2500 numbered formulae. The book serves as a basic reference for researchers, graduate students, and people doing applied work with Brownian motion and diffusions, and can be used as a source of explicit examples when teaching stochastic processes.
