Download or read book Lectures from Markov Processes to Brownian Motion written by Kai Lai Chung and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book as the Course, and may be considered as a general background; its specific use is limited to the mate rial on discrete parameter martingale theory cited in § 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained.
Download or read book Markov Processes Brownian Motion and Time Symmetry written by Kai Lai Chung and published by Springer Science & Business Media. This book was released on 2005-07-15 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.
Download or read book Green Brown And Probability written by Kai Lai Chung and published by World Scientific. This book was released on 1995-10-18 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume shows modern probabilistic methods in action: Brownian Motion Process as applied to the electrical phenomena investigated by Green et al., beginning with the Newton-Coulomb potential and ending with solutions by first and last exits of Brownian paths from conductors.
Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Markov Processes Brownian Motion and Time Symmetry written by Kai Lai Chung and published by Springer Science & Business Media. This book was released on 2006-01-18 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.
Download or read book Aspects of Brownian Motion written by Roger Mansuy and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.
Download or read book Some Aspects of Brownian Motion written by Marc Yor and published by Birkhäuser. This book was released on 2012-12-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993. Part I, the elder brother of the present book [Part II], aimed at the computation, as explicitly as possible, of a number of interesting functionals of Brownian motion. It may be natural that Part II, the younger brother, looks more into the main technique with which Part I was "working", namely: martingales and stochastic calculus. As F. Knight writes, in a review article on Part I, in which research on Brownian motion is compared to gold mining: "In the days of P. Levy, and even as late as the theorems of "Ray and Knight" (1963), it was possible for the practiced eye to pick up valuable reward without the aid of much technology . . . Thereafter, however, the rewards are increasingly achieved by the application of high technology". Although one might argue whether this golden age is really foregone, and discuss the "height" of the technology involved, this quotation is closely related to the main motivations of Part II: this technology, which includes stochastic calculus for general discontinuous semi-martingales, enlargement of filtrations, . . .
Download or read book Stochastic Processes written by Kiyosi Ito and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
Download or read book Essentials of Stochastic Processes written by Richard Durrett and published by Springer. This book was released on 2016-11-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.
Download or read book Stochastic Processes written by S. R. S. Varadhan and published by American Mathematical Soc.. This book was released on 2007 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a brief introduction to stochastic processes studying certain elementary continuous-time processes. The text describes the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps.
Download or read book Brownian Motion written by T. Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the publication of the Japanese edition of this book, several inter esting developments took place in the area. The author wanted to describe some of these, as well as to offer suggestions concerning future problems which he hoped would stimulate readers working in this field. For these reasons, Chapter 8 was added. Apart from the additional chapter and a few minor changes made by the author, this translation closely follows the text of the original Japanese edition. We would like to thank Professor J. L. Doob for his helpful comments on the English edition. T. Hida T. P. Speed v Preface The physical phenomenon described by Robert Brown was the complex and erratic motion of grains of pollen suspended in a liquid. In the many years which have passed since this description, Brownian motion has become an object of study in pure as well as applied mathematics. Even now many of its important properties are being discovered, and doubtless new and useful aspects remain to be discovered. We are getting a more and more intimate understanding of Brownian motion.
Download or read book Lectures on the Coupling Method written by Torgny Lindvall and published by Courier Corporation. This book was released on 2012-08-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.
Download or read book Brownian Motion written by René L. Schilling and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-09-07 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.
Download or read book Cycle Representations of Markov Processes written by Sophia L. Kalpazidou and published by Springer Science & Business Media. This book was released on 2007-03-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a prototype providing new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. These processes have special and important properties through the interaction between the geometric properties of the trajectories and the algebraic characterization of the Markov process. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. In particular, it provides an entirely new approach to infinite electrical networks and their applications in topics as diverse as random walks, the classification of Riemann surfaces, and to operator theory. The second edition of this book adds new advances to many directions, which reveal wide-ranging interpretations of the cycle representations like homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The versatility of these interpretations is consequently motivated by the existence of algebraic-topological principles in the fundamentals of the cycle representations. This book contains chapter summaries as well as a number of detailed illustrations. Review of the earlier edition: "This is a very useful monograph which avoids ready ways and opens new research perspectives. It will certainly stimulate further work, especially on the interplay of algebraic and geometrical aspects of Markovian dependence and its generalizations." Math Reviews
Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Download or read book Markov Processes Gaussian Processes and Local Times written by Michael B. Marcus and published by Cambridge University Press. This book was released on 2006-07-24 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
Download or read book Brownian Motion Martingales and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
