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Springer eBooks

From two stochastic optimal control problems to the Schrodinger equation

Katherine A. Kime, Austin Blaquière

Published Feb 6, 2006• 11 citations
Publisher
DOI
10.1007/bfb0041195

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The quantum-mechanical formulation of a class of stochastic optimal control problems is investigated and two versions of non-linear Schrödinger equation are derived. First, a wave-function is introduced which connects the probability density function of a diffusion process with the minimum cost functional of the stochastic optimal control problem associated with the diffusion process. It is then demonstrated that this wave-function satisfies a kind of Schrödinger-Langevin equation in quantum physics. Finally, the probabilistic interpretation of the wave-function is discussed.