Mathematical Sciences: Asymptotic Behavior of Brownian      Motion and Random Walk Processes
{'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 principal investigator will continue his study of the                  upper and lower tail behavior of vector valued Brownian motion.                 Results in this direction can be used for estimating the behavior               of other Gaussian processes such as a two parameter Kiefer                      process.  The oscillatory behavior of these processes is studied                via the discrepancy between collections of sample paths and                     certain non-random set functions.  The non-random set functions                 are metric entropy of balls in the reproducing kernel Hilbert                   space of the Brownian motion.  Error rates for the convergence of               the processes to their cluster sets and the approximate density                 of sample path collections is established.  The research will                   contribute to the observable regularities within a widely-studied               framework involving long-time chaos.
{'FirstName': 'Victor', 'LastName': 'Goodman', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Victor W Goodman', 'EmailAddress': 'goodmanv@indiana.edu', 'NSF_ID': '000406430', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Indiana University', 'CityName': 'BLOOMINGTON', 'ZipCode': '474057000', 'PhoneNumber': '3172783473', 'StreetAddress': '107 S INDIANA AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'IN09', 'ORG_UEI_NUM': 'YH86RTW2YVJ4', 'ORG_LGL_BUS_NAME': 'TRUSTEES OF INDIANA UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'YH86RTW2YVJ4'}
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{'Code': '1263', 'Text': 'PROBABILITY'}
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