This monograph uses Robinson's infinitesimal (i.e., nonstandard) analysis to study stochastic integral equations with respect to a Brownian motion. By using a combination of standard and infinitesimal methods, we obtain new results about stochastic integral equations which can b…
The purpose of this paper is to construct Brownian motion on a reasonably general class of self-similar fractals. To this end, I introduce an axiomatically defined class of "nested fractals", which satisfy certain symmetry and connectivity conditions, and which also are (in the …
This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems ? those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promo…
One of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed nonstandard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this first …
"One of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed non-standard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this firs…
