Mathematical Sciences: Research on Optimal Stochastic       Control and Related Topics
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{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
This project includes several subprojects and represents quite a            vast research program in the area of stochastic control, stochastic             processes and nonlinear filtering.                                                  The research in stochastic control proposed by Professor Fleming            is focused on the questions related to the existence and properties             of solutions to the Hamilton-Jacobi equation. One outstanding                   question is whether given the Hamiltonian function there is a                   corresponding stochastic control problem for diffusion processes                leading to this function. Recently, Fleming and Souganidis                      introduced a new formulation of a stochastic differential game,                 based on a new deterministic approach to differential games, which              leads to the solution of this problem by replacing the control                  problem by a game problem. Fleming also intends to work on a number             of open problems related to viscosity solutions for nonlinear first-            order partial differential equations. Among open problems to be                 considered are the theory of discontinuous viscosity solutions, and             the application of duality theorems of convex analysis to                       approximate the value function of the Hamilton-Jacobi equation.                     The research in stochastic processes centers on the exit problem            of Freidlin-Wentsel theory. Fleming introduced the stochastic                   control approach to this problem and applied an asymptotic expansion            to the dynamic programming equation obtained after a logarythmic                transformation. This enables him to compute exit probabilities from             the expansion. These expansions are of interest for problems of rare            overloads in communications channels.                                               On the nonlinear filtering problem, Fleming proposes to use some            asymptotic techniques to describe analytically the structure of the             nonlinear filter for small intensities of noise in the output                   equation.                                                                           Stochastic control is a branch of applied mathematics and                   engineering system theory that deals with control of dynamical                  systems in situations involving random inputs and measurement noise.            The mathematical tools involved in this research are the theory of              stochastic processes, nonlinear partial differential equations,                 asymptotic methods and numerical methods.
{'FirstName': 'Wendell', 'LastName': 'Fleming', 'PI_MID_INIT': 'H', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Wendell H Fleming', 'EmailAddress': 'whf@cfm.brown.edu', 'NSF_ID': '000290307', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Brown University', 'CityName': 'PROVIDENCE', 'ZipCode': '029129100', 'PhoneNumber': '4018632777', 'StreetAddress': '1 PROSPECT ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Rhode Island', 'StateCode': 'RI', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'RI01', 'ORG_UEI_NUM': 'E3FDXZ6TBHW3', 'ORG_LGL_BUS_NAME': 'BROWN UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1454', 'Text': 'SYSTEMS THEORY'}]
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