Investigations On The Theory Of The Brownian Movement

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Author: Albert Einstein
Publisher: Courier Corporation
ISBN: 9780486603049
Size: 46.32 MB
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Investigations On The Theory Of The Brownian Movement by Albert Einstein


Original Title: Investigations On The Theory Of The Brownian Movement

Five early papers evolve theory that won Einstein a Nobel Prize: "Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat"; "On the Theory of the Brownian Movement"; "A New Determination of Molecular Dimensions"; "Theoretical Observations on the Brownian Motion"; and "Elementary Theory of the Brownian Motion."

Brownian Motion

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Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Size: 38.77 MB
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Brownian Motion by Peter Mörters


Original Title: Brownian Motion

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.

Dynamical Theories Of Brownian Motion

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Author: Edward Nelson
Publisher: Princeton University Press
ISBN: 0691079501
Size: 14.31 MB
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Dynamical Theories Of Brownian Motion by Edward Nelson


Original Title: Dynamical Theories Of Brownian Motion

These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.

Brownian Motion And Stochastic Calculus

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Author: Ioannis Karatzas
Publisher: Springer
ISBN: 1461209498
Size: 36.53 MB
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Brownian Motion And Stochastic Calculus by Ioannis Karatzas


Original Title: Brownian Motion And Stochastic Calculus

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.

Selected Aspects Of Fractional Brownian Motion

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Author: Ivan Nourdin
Publisher: Springer Science & Business Media
ISBN: 884702823X
Size: 55.32 MB
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Selected Aspects Of Fractional Brownian Motion by Ivan Nourdin


Original Title: Selected Aspects Of Fractional Brownian Motion

Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

Green Brown And Probability Brownian Motion On The Line

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Author: Kai Lai Chung
Publisher: World Scientific
ISBN: 9789810246907
Size: 76.57 MB
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Green Brown And Probability Brownian Motion On The Line by Kai Lai Chung


Original Title: Green Brown And Probability Brownian Motion On The Line

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.

Markov Processes Brownian Motion And Time Symmetry

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Author: Kai Lai Chung
Publisher: Springer Science & Business Media
ISBN: 9780387220260
Size: 38.12 MB
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Markov Processes Brownian Motion And Time Symmetry by Kai Lai Chung


Original Title: Markov Processes Brownian Motion And Time Symmetry

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.

Brownian Motion

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Author: Mark A. McKibben
Publisher:
ISBN: 9781634836821
Size: 24.49 MB
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Brownian Motion by Mark A. McKibben


Original Title: Brownian Motion

The fields of study in which random fluctuations arise and cannot be ignored are as disparate and numerous as there are synonyms for the word noise. In the nearly two centuries following the discovery of what has come to be known as Brownian motion, named in homage to botanist Robert Brown, scientists, engineers, financial analysts, mathematicians, and literary authors have posited theories, created models, and composed literary works which have accounted for environmental noise. This volume offers a glimpse into the ways in which Brownian motion has crept into a myriad of fields of study through fifteen distinct chapters written by mathematicians, physicists, and other scholars. The intent is to especially highlight the vastness of scholarly work that explains various facets of Nature made possible by one scientists curiosity sparked by observing sporadic movement of specks of pollen under a microscope in a 19th century laboratory.

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