Other Applications
Other results were received along the line of reinterpreting or reproving previously known results. Of particular interest is Kamae's proof of the individual ergodic theorem or van den Dries and Wilkie's treatment of Gromov's theorem on groups of polynomial growth. NSA was used by Larry Manevitz and Shmuel Weinberger to prove a result in algebraic topology.
The real contributions of non-standard analysis lie however in the concepts and theorems that utilizes the new extended language of non-standard set theory. Among the list of new applications in mathematics there are new approaches to probability hydrodynamics, measure theory, nonsmooth and harmonic analysis, etc.
There are also applications of non-standard analysis to the theory of stochastic processes, particularly constructions of Brownian motion as random walks. Albeverio et-al have an excellent introduction to this area of research.
Read more about this topic: Non-standard Analysis