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25 Remote Warehouse Mathematics- Modeling

Other titles in the Lecture Notes in Mathematics series:

Lecture Notes in Mathematics #2067: Stochastic Calculus with Infinitesimals

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Lecture Notes in Mathematics #2067: Stochastic Calculus with Infinitesimals Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of 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 Black-Scholes model.- 7 A radically elementary theory of Itô 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 Lévy processes.- 10 Final remarks.

Product Details

ISBN:
9783642331480
Author:
Herzberg, Frederik
Publisher:
Springer
Author:
Herzberg, Frederik S.
Subject:
Logic
Subject:
03H05; 60G05; 91B25; 81Q30; 60G51; 60H05; 60H10
Subject:
Feynman Path Integral
Subject:
Internal Set Theory
Subject:
Asset pricing
Subject:
infinitesimals
Subject:
Mathematical Logic and Foundations
Subject:
Probability Theory and Stochastic Processes
Subject:
Game Theory, Economics, Social and Behav. Sciences
Subject:
Mathematical Physics
Subject:
Mathematics-Modeling
Copyright:
Edition Description:
2013
Series:
Lecture Notes in Mathematics
Series Volume:
2067
Publication Date:
20121123
Binding:
TRADE PAPER
Language:
English
Pages:
130
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Electricity » General Electronics
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Lecture Notes in Mathematics #2067: Stochastic Calculus with Infinitesimals New Trade Paper
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