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Stochastic Calculus with Infinitesimals / by Frederik Herzberg.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2366,2368-2379,2381-2382 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Herzberg, Frederik, 1981- author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2067.
- Lecture Notes in Mathematics, 0075-8434 ; 2067
- Language:
- English
- Subjects (All):
- Logic, Symbolic and mathematical.
- Distribution (Probability theory).
- Economics.
- Mathematics.
- Mathematical Logic and Foundations.
- Probability Theory and Stochastic Processes.
- Economic Theory/Quantitative Economics/Mathematical Methods.
- Game Theory, Economics, Social and Behav. Sciences.
- Mathematical Physics.
- Local Subjects:
- Mathematical Logic and Foundations.
- Probability Theory and Stochastic Processes.
- Economic Theory/Quantitative Economics/Mathematical Methods.
- Game Theory, Economics, Social and Behav. Sciences.
- Mathematical Physics.
- Physical Description:
- 1 online resource (XVIII, 112 pages).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
- System Details:
- text file PDF
- Summary:
- 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 9783642331497
- Access Restriction:
- Restricted for use by site license.
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