Mathematical Sciences: Some Problems in Stochastic Analysis
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{'SignBlockName': 'Peter Arzberger', 'PO_EMAI': None, 'PO_PHON': None}
The first part of this research will deal with Brownian                    motion on negatively curved manifolds.  The investigator intends                to find the Martin boundary for strongly negatively curved                      manifolds, and identify the bounded solutions of the heat                       equation.  Also, conditions will be found under which harmonic                  measure on such manifolds is absolutely continuous with respect                 to angular measure, in polar coordinates.                                            The second problem will deal with a nonlinear stochastic                   version of the heat equation.  The investigator will study the                  rate at which the solution decays to zero.  This will be a first                step toward studying the qualitative behavior of such equations.                     The third problem will deal with the law of iterated                       logarithm for analytic functions, recently obtained by Markov.  A               version of Chung's law of the iterated logarithm will be sought                 for analytic functions.  From this, packing dimension of the                    support of harmonic measure might be found in the same way as                   Markov found the Hausdorff dimension of the support.
{'FirstName': 'Carl', 'LastName': 'Mueller', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Carl E Mueller', 'EmailAddress': 'carl0000mueller@gmail.com', 'NSF_ID': '000445882', '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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