說明 
1 online resource (xviii, 112 p.) 
系列 
Lecture notes in mathematics, 16179692 ; 2067


Lecture notes in mathematics (SpringerVerlag) ; 2067

附註 
Infinitesimal calculus, consistently and accessibly  Radically elementary probability theory  Radically elementary stochastic integrals  The radically elementary girsanov theorem and the diffusion invariance principle  Excursion to financial economics: a radically elementary approach to the fundamental theorems of asset pricing  Excursion to financial engineering: volatility invariance in the blackScholes model  A radically elementary theory of itô diffusions and associated partial differential equations  Excursion to mathematical physics: a radically elementary definition of feynman path integrals  A radically elementary theory of lévy processes  Final remarks 

Includes bibliographical references and index 

Description based on online resource; title from PDF title page (SpringerLink, viewed Nov. 19, 2012) 

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 continuoustime 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 BlackScholes theory of option pricing and the Feynman path integral) are also discussed in the book 
主題 
Stochastic processes


Logic, Symbolic and mathematical


(DE588)41322721 (DE603)085475165 Stochastische Analysis gnd


Logic, Symbolic and mathematical. fast (OCoLC)fst01002068


Stochastic processes. fast (OCoLC)fst01133519


Electronic books

