دانلود کتاب Stochastic calculus with infinitesimals

"This short monograph develops basic stochastic analysis ... and select applications in the framework of Edward Nelson's 'Radically elementary probability theory' (Annals of mathematics studies, 117, Princeton, NJ : Princeton University Press, 1987). This approach requires neither measure-theoretic probability theory nor functional analysis, but is based on a rigorous, yet elementary use of unlimited natural numbers and infinitesimals." Read more... 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 Black-Scholes 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 -- -- Excursion to logic: some remarks on the metamathematics of minimal internal set theory -- -- Robinsonian vs. minimal nonstandard analysis