Stochastic Calculus with Infinitesimals
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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2013, 2013
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| Edition: | 1st ed. 2013 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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