Mathematical Sciences: Probability Theory
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Stephen M. Samuels', 'PO_EMAI': None, 'PO_PHON': None}
The principal investigator will work on the boundary lines                 of probability theory and classical analysis.  The process of                   interest is Doob's h process.  It is a conditional Brownian                     motion starting at a point in a domain and conditioned to exit                  the domain at a given point or to hit a given point before                      exiting the domain.  The h processes have close connections to a                number of non-probabilistic quantities in several areas of                      analysis.  Thus the study of h processes simultaneously sheds                   more light on the probabilistic behavior of the conditional                     Brownian motion and provides a vehicle to apply probabilistic                   results to various area in analysis.  The specific topics of                    study include martingale transforms, connections between the                    Cranston-McConnell theorem and the first eigenvalue, and the                    integrability of the first eigenfunction on unbounded domains.
{'FirstName': 'Burgess', 'LastName': 'Davis', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Burgess J Davis', 'EmailAddress': 'bdavis@stat.purdue.edu', 'NSF_ID': '000285884', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}, {'Code': '1263', 'Text': 'PROBABILITY'}]
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