Stochastic Calculus with Infinitesimals Lecture Notes in Mathematics

"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."--