The infinite-dimensional Ornstein-Uhlenbeck process v is constructed from Brownian motion on the infinite-dimensional sphere SN-1(1) (the Wiener sphere) - or equivalently, by rescaling, on - which is defined for infinite N by nonstandard analysis. This gives rigorous sense to the informal idea...

In this paper we develop a new notion of convergence for discussing the relationship between discrete and continuous financial models, "D"-super-2-convergence. This is stronger than weak convergence, the commonly used mode of convergence in the finance literature. We show that...

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from...