Title :
Schrödinger equation with quartic potential and nonlinear filtering problem
Author :
Chang, Der-Chen ; Yau, Stephen S T ; Lin, Ke-Pao
Author_Institution :
Dept. of Math., Georgetown Univ., Washington, DC, USA
Abstract :
The celebrated work of Yau and Yau 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 Schrodinger equation. In this paper, we shall describe the fundamental solution of this Schrodinger equation with quartic potential.
Keywords :
Schrodinger equation; nonlinear filters; Duncan Mortensen Zakai equation; Kolmogorov type equation; Schrodinger equation; Yau filtering system; nonlinear filtering problem; off time solution; quartic potential; Algebra; Differential algebraic equations; Differential equations; Filtering algorithms; Filtering theory; Mathematics; Nonlinear equations; Partial differential equations; Polynomials; Quantum mechanics;
Conference_Titel :
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5400128
