Includes bibliographical references (pages 107-110) and index.
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.
"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."-- Abstract.