Properties of Linear Brownian Motion with Variable Drift
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Total Pages | : 71 |
Release | : 2012 |
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Author | : |
Publisher | : |
Total Pages | : 71 |
Release | : 2012 |
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Author | : Peter Mörters |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2010-03-25 |
Genre | : Mathematics |
ISBN | : 1139486578 |
This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.
Author | : Andrei N. Borodin |
Publisher | : Springer Science & Business Media |
Total Pages | : 710 |
Release | : 2015-07-14 |
Genre | : Mathematics |
ISBN | : 9783764367053 |
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.
Author | : David Applebaum |
Publisher | : Cambridge University Press |
Total Pages | : 235 |
Release | : 2019-08-15 |
Genre | : Mathematics |
ISBN | : 1108483097 |
Provides a graduate-level introduction to the theory of semigroups of operators.
Author | : Jean-François Le Gall |
Publisher | : Springer |
Total Pages | : 282 |
Release | : 2016-04-28 |
Genre | : Mathematics |
ISBN | : 3319310895 |
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 | : Marc Yor |
Publisher | : Springer Science & Business Media |
Total Pages | : 213 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642566340 |
This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between 1988 and 1998. Throughout the volume, connections with more recent studies involving exponential functionals of Lévy processes are indicated. Some papers originally published in French are made available in English for the first time.
Author | : Andrei Borodin |
Publisher | : Birkhäuser |
Total Pages | : 478 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034876521 |
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 | : Kai Lai Chung |
Publisher | : World Scientific |
Total Pages | : 184 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9789810246907 |
This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity ? Green's formula for solving the boundary value problem of Laplace equations and the Newton-Coulomb potential.Part II of the book comprises lecture notes based on a short course on ?Brownian Motion on the Line? which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.
Author | : Simo Särkkä |
Publisher | : Cambridge University Press |
Total Pages | : 327 |
Release | : 2019-05-02 |
Genre | : Business & Economics |
ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author | : Ioannis Karatzas |
Publisher | : Springer |
Total Pages | : 490 |
Release | : 2014-03-27 |
Genre | : Mathematics |
ISBN | : 1461209498 |
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.