Schrödinger equation with quartic potential and nonlinear filtering problem

The celebrated work of Yau and Yau [1] solved the nonlinear filtering problem in theory in the following manner. They reduced the problem of solving the Duncan-Mortensen-Zakai equation in real-time to the off-time solution of a Kolmogorov type equation. For the Yau filtering system, this Kolmogorov equation can be transformed as the Schrödinger equation. In this paper, we shall describe the fundamental solution of this Schrödinger equation with quartic potential.

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