Mathematical Sciences: Applications of Stochastic Calculus  of Variations and Skorohod's Integral to Stochastic Systems
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
The investigator intends to do research on two topics using the             methods of the stochastic calculus of variations. The first topic               concerns the analysis of "acausal" stochastic differential equations            driven by Brownian motion. Recently, Nualart and Pardoux used the               stochastic calculus of variations to develop a calculus for the                 Skorokhod integral, which is an integral with respect to Brownian               motion for integrands not necessarily adapted to the past of the                Brownian motion. This should allow one to study equations containing            "acausal" features, that is exhibiting dependence not only on the               past but also on the future. Professor Ocone intends to undertake               research in this direction. The second topic concerns the analysis              of the probability distributions of solutions of stochastic partial             differential equations. This study has implications for nonlinear               filtering theory. In this project the investigator wishes to                    continue the line of investigation that leads to a study of                     regularity of densities for linear functionals on solutions to                  stochastic partial differential equations. He will also study the               nonlinear filtering problem, and attempt to relate Wiener space                 gradients of conditional distributions of nonlinear filters to the              issue of finite dimensional computability of filters. This is a                 theoretical work where computability is characterized by the                    existence of certain finite dimensional stochastic differential                 equation that governs certain conditional expectations. There is  a             possibility that the investigator can relate computability to                   certain rank conditions for Frechet derivatives of certain maps.                    This research belongs to a larger research effort on stochastic             differential equations and filtering problems that is now an active             area in applied probability.
{'FirstName': 'Daniel', 'LastName': 'Ocone', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Daniel Ocone', 'EmailAddress': None, 'NSF_ID': '000209591', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Rutgers University New Brunswick', 'CityName': 'NEW BRUNSWICK', 'ZipCode': '089018559', 'PhoneNumber': '8489320150', 'StreetAddress': '3 RUTGERS PLZ', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'M1LVPE5GLSD9', 'ORG_LGL_BUS_NAME': 'RUTGERS, THE STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
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