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Stochastic Calculus with Infinitesimals

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

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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.

Stochastic Calculus with Infinitesimals

2012-11-07 Mathematics
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Release : 2012-11-07
Genre : Mathematics
Kind : eBook
Book Rating : 503/5 ( reviews)

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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 2012-11-07. 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.

Foundations of Infinitesimal Stochastic Analysis

2011-08-18 Computers
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Release : 2011-08-18
Genre : Computers
Kind : eBook
Book Rating : 421/5 ( reviews)

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Book Synopsis Foundations of Infinitesimal Stochastic Analysis by : K.D. Stroyan

Download or read book Foundations of Infinitesimal Stochastic Analysis written by K.D. Stroyan. This book was released on 2011-08-18. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

Quantum Stochastic Calculus Using Infinitesimals

2001
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Release : 2001
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Quantum Stochastic Calculus Using Infinitesimals by : Martin Leitz-Martini

Download or read book Quantum Stochastic Calculus Using Infinitesimals written by Martin Leitz-Martini. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt:

Calculus Set Free

2021-11-30 Calculus
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Release : 2021-11-30
Genre : Calculus
Kind : eBook
Book Rating : 591/5 ( reviews)

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Book Synopsis Calculus Set Free by :

Download or read book Calculus Set Free written by . This book was released on 2021-11-30. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a significant burden of entry into STEM disciplines. This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple rapid response questions to the occasional exercise meant to test knowledge. While some exercises require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified answers, hints, or alternative answers. Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on difficult theoretical calculus.

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