Radically Elementary Probability Theory Am 117 Volume 117

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Stochastic Calculus With Infinitesimals

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Author : Frederik S. Herzberg
language : en
Publisher: Springer
Release Date : 2012-11-06

Stochastic Calculus With Infinitesimals written by Frederik S. Herzberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.

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

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Author : Nigel J Cutland
language : en
Publisher: CRC Press
Release Date : 2020-01-30

Developments In Nonstandard Mathematics written by Nigel J Cutland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.

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

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Author : Erwin Bolthausen
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Seminar On Stochastic Analysis Random Fields And Applications written by Erwin Bolthausen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Nonstandard Analysis

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Author : Karl Kuhlemann
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-16

Nonstandard Analysis written by Karl Kuhlemann and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-16 with Mathematics categories.

Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard analysis and discusses logical, model-theoretic, and set-theoretic investigations to reveal possible mathematical reasons that may lead to reservations about nonstandard analysis. Also various foundational positions as well as ontological, epistemological, and application-related issues are addressed. It turns out that the one-sided preference for standard analysis is justified neither from a didactic, mathematical nor philosophical point of view. Thus, the book is especially valuable for students and instructors of analysis who are also interested in the foundations of their subject.

Diffusion Quantum Theory And Radically Elementary Mathematics Mn 47

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Author : William G. Faris
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08

Diffusion Quantum Theory And Radically Elementary Mathematics Mn 47 written by William G. Faris and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.

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.

Nonlinear Dynamics New Directions

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Author : Hernán González-Aguilar
language : en
Publisher: Springer
Release Date : 2015-03-09

Nonlinear Dynamics New Directions written by Hernán González-Aguilar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-09 with Technology & Engineering categories.

This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics · Features recent developments on large deviations for higher-dimensional maps, a study of measures resisting multifractal analysis and a overview of complex Kleninan groups · Includes thorough review of recent findings that emphasize new development prospects

Probability

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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-30

Probability written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-30 with Mathematics categories.

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Subject Guide To Books In Print

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Author :
language : en
Publisher:
Release Date : 1996

Subject Guide To Books In Print written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with American literature categories.

Probability Theory

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Author : E. T. Jaynes
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-10

Probability Theory written by E. T. Jaynes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-10 with Mathematics categories.

Index.

Applied Science Technology Index

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Author :
language : en
Publisher:
Release Date : 1996

Applied Science Technology Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Engineering categories.