Stochastic Calculus with Infinitesimals

• Main Author: Herzberg, Frederik. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2067
• Subjects: Mathematics.; Logic, Symbolic and mathematical.; Distribution (Probability theory).; Mathematical Logic and Foundations.; Probability Theory and Stochastic Processes.; Game Theory, Economics, Social and Behav. Sciences.; Mathematical Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-33149-7

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) a...

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 It ̥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 Lv̌y processes
• 10 Final remarks.