Nonlinear filtering and time varying Schrodinger equation |
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Authors: | Shing-Tung Yau Yau SS-T |
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Institution: | Harvard Univ., Boston, MA, USA; |
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Abstract: | Based on our previous work we have successfully reduced the nonlinear filtering problem for Yau filtering system to the time-varying Schrodinger equation. In order to solve the nonlinear filtering problem, one needs to solve the time-varying Schrodinger equation with an arbitrary initial condition. We then solve the time-varying Schrodinger equation by constructing the fundamental solution explicitly via a system of nonlinear ODES in case the potential is quadratic in state variables. This system of nonlinear ODES is solved explicitly by the power series method. |
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