Stochastic Calculus with Infinitesimals

• Κύριος συγγραφέας: Herzberg, Frederik (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Σειρά: Lecture Notes in Mathematics, 2067
• Θέματα: Mathematics.; Game theory.; Mathematical logic.; Probabilities.; Mathematical physics.; Economic theory.; Mathematical Logic and Foundations.; Probability Theory and Stochastic Processes.; Economic Theory/Quantitative Economics/Mathematical Methods.; Game Theory, Economics, Social and Behav. Sciences.; Mathematical Physics.

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...

Πίνακας περιεχομένων:

• 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.