The methods of stochastic analysis have found applications in many fields, some far removed from probability itself. This is the case for both harmonic analysis and differential equations. As an example, the problem of determining interior temperature from the boundary distribution has an appealing and significant solution through probability theory. One introduces an infinite dimensional space of random paths, which provides a richer structure for many problems than the customary finite dimensional Euclidean space. It is in this context, the use of stochastic reasoning to improve our understanding of functions on Euclidean space, that Professor Gundy's research takes place. That is to say, he specializes in problems in the margin between probability theory and classical analysis. He has utilized martingale theory to study orthogonal polynomials, and he has made major contributions to function theory, Hardy space analysis, and Brownian motion. The current proposal concerns the extension of these ideas to the infinite dimensional space of continuous functions on Wiener space.
