Mathematical Sciences: Martingale Theory and Analysis
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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.
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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