Mathematical Sciences: Decoupling, Stochastic Integration   and Representation of Banach-Space-Valued Martingales
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
Stochastic integration is a very useful analytic tool in                   applications of many models to real life.  In recent years, the                 classical theory of stochastic integration has been generalized                 to other cases.  This makes it possible to use more general                     models.  This research will continue to study stochastic                        integration with the help of some special techniques called the                 decoupling inequalities.                                                             In the standard setting of a stochastic integral, the                      integrant and the integrating stochastic process are independent.               Decoupling inequalities mainly try to handle the lack of such                   independence by separating the independent part and bounding the                remaining part.  This research will study stochastic integration                with respect to infinite dimensional stochastic processes with                  the help of the decoupling inequalities.  It will also study the                applications to U-statistics.
{'FirstName': 'Terry', 'LastName': 'McConnell', 'PI_MID_INIT': 'R', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Terry R McConnell', 'EmailAddress': None, 'NSF_ID': '000161295', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Syracuse University', 'CityName': 'SYRACUSE', 'ZipCode': '13244', 'PhoneNumber': '3154432807', 'StreetAddress': '900 S CROUSE AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '22', 'CONGRESS_DISTRICT_ORG': 'NY22', 'ORG_UEI_NUM': 'C4BXLBC11LC6', 'ORG_LGL_BUS_NAME': 'SYRACUSE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126300', 'Text': 'PROBABILITY'}
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