Mathematical Sciences: Multidimensional Diffusions and      Applications
{'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 is one of the leading authorities in the                  world on reflected Brownian motions in polyhedral domains.  Such                processes arise as limits of many practical models, particularly                in queuing networks.  Investigator's previous results will be                   extended to three and more dimensions, making the models more                   applicable.                                                                          The project will continue to investigate the local path                    properties of Brownian excursions in Lipschitz domains.  In                     particular, to investigate the distributional properties, it is                 conjectured that the excursions from tangent hyperplanes will be                similar to the excursions from hyperplanes.                                          Diffusions with singular drifts or discontinuous diffusion                 coefficients arise in many important area of applications such as               filtering theory and stochastic control theory.  The investigator               will explore the questions of existence and uniqueness of such                  diffusions as well as the return to origin.
{'FirstName': 'Ruth', 'LastName': 'Williams', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ruth J Williams', 'EmailAddress': 'williams@math.ucsd.edu', 'NSF_ID': '000459574', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-San Diego', 'CityName': 'LA JOLLA', 'ZipCode': '920930021', 'PhoneNumber': '8585344896', 'StreetAddress': '9500 GILMAN DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '50', 'CONGRESS_DISTRICT_ORG': 'CA50', 'ORG_UEI_NUM': 'UYTTZT6G9DT1', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, SAN DIEGO', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1263', 'Text': 'PROBABILITY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8722351.xml'}