Mathematical Sciences: Diffusions and Potential Theory,     Diffusions on Manifolds
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Peter Arzberger', 'PO_EMAI': None, 'PO_PHON': None}
The investigator will examine the properties of diffusions                 on manifolds and diffusion corresponding to elliptic divergence                 form operators.  Diffusion processes provide widely used models                 especially in Physics.  Both the analytic and the probabilistic                 tools will be used to seek solutions to these important problems.               On manifolds, the smoothness of the exit distribution of Brownian               motion will be studied.  On special structures, the investigator                will study the asymptotic behavior of conditioned Brownian                      motion.  For diffusions arising from elliptic divergence form                   operators, transformation of drift formulae, conditional gauge                  theorems and sample path properties will be studied.
{'FirstName': 'Michael', 'LastName': 'Cranston', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Michael Cranston', 'EmailAddress': 'mcransto@math.uci.edu', 'NSF_ID': '000387002', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Rochester', 'CityName': 'ROCHESTER', 'ZipCode': '146113847', 'PhoneNumber': '5852754031', 'StreetAddress': '910 GENESEE ST', 'StreetAddress2': 'STE 200', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '25', 'CONGRESS_DISTRICT_ORG': 'NY25', 'ORG_UEI_NUM': 'F27KDXZMF9Y8', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ROCHESTER', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1263', 'Text': 'PROBABILITY'}
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