Stochastic calculus with infinitesimals
 Responsibility
 Frederik S. Herzberg.
 Language
 English.
 Publication
 Heidelberg : Springer, [2013]
 Copyright notice
 ©2013
 Physical description
 xviii, 112 pages ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2067.
Access
Available online
 www.springerlink.com
 dx.doi.org SpringerLink
Math & Statistics Library
Stacks
Call number  Status 

QA3 .L28 V.2067  Unknown 
More options
Creators/Contributors
 Author/Creator
 Herzberg, Frederik, 1981 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 107110) and index.
 Contents

 1 Infinitesimal calculus, consistently and accessibly. 2 Radically elementary probability theory. 3 Radically elementary stochastic integrals. 4 The radically elementary Girsanov theorem and the diffusion invariance principle. 5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing. 6 Excursion to financial engineering: Volatility invariance in the BlackScholes model. 7 A radically elementary theory of Ito diffusions and associated partial differential equations. 8 Excursion to mathematical physics: A radically elementary definition of Feynman path integrals. 9 A radically elementary theory of Levy processes. 10 Final remarks.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 continuoustime 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 BlackScholes theory of option pricing and the Feynman path integral) are also discussed in the book.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Series
 Lecture notes in mathematics, 00758434 ; 2067
 ISBN
 9783642331480 (paperback)
 3642331483 (paperback)