Share

Radically Elementary Probability Theory. (AM-117), Volume 117

2016-03-02 Mathematics
Download Radically Elementary Probability Theory. (AM-117), Volume 117 PDF Online Free

Author :
Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 141/5 ( reviews)

GET EBOOK


Book Synopsis Radically Elementary Probability Theory. (AM-117), Volume 117 by : Edward Nelson

Download or read book Radically Elementary Probability Theory. (AM-117), Volume 117 written by Edward Nelson. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

Stochastic Calculus with Infinitesimals

2012-11-06 Mathematics
Download Stochastic Calculus with Infinitesimals PDF Online Free

Author :
Release : 2012-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 491/5 ( reviews)

GET EBOOK


Book Synopsis Stochastic Calculus with Infinitesimals by : Frederik S. Herzberg

Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg. This book was released on 2012-11-06. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.

Developments in Nonstandard Mathematics

2020-01-30 Mathematics
Download Developments in Nonstandard Mathematics PDF Online Free

Author :
Release : 2020-01-30
Genre : Mathematics
Kind : eBook
Book Rating : 821/5 ( reviews)

GET EBOOK


Book Synopsis Developments in Nonstandard Mathematics by : Nigel J Cutland

Download or read book Developments in Nonstandard Mathematics written by Nigel J Cutland. This book was released on 2020-01-30. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.

Seminar on Stochastic Analysis, Random Fields and Applications

2012-12-06 Mathematics
Download Seminar on Stochastic Analysis, Random Fields and Applications PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 264/5 ( reviews)

GET EBOOK


Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications by : Erwin Bolthausen

Download or read book Seminar on Stochastic Analysis, Random Fields and Applications written by Erwin Bolthausen. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied stochastic analysis and random fields form the subject of this book. The collection of articles on these topics represent the state of the art of the research in the field, with particular attention being devoted to stochastic models in finance. Some are review articles, others are original papers; taken together, they will apprise the reader of much of the current activity in the area.

Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)

2014-09-08 Mathematics
Download Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) PDF Online Free

Author :
Release : 2014-09-08
Genre : Mathematics
Kind : eBook
Book Rating : 255/5 ( reviews)

GET EBOOK


Book Synopsis Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) by : William G. Faris

Download or read book Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) written by William G. Faris. This book was released on 2014-09-08. Available in PDF, EPUB and Kindle. Book excerpt: Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

You may also like...