A Stochastic Control Verification Theorem for the Dequantized Schrödinger Equation Not Requiring a Duration Restriction
A Stochastic Control Verification Theorem for the Dequantized Schrödinger Equation Not Requiring a Duration Restriction
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不需要时长限制的反量化薛定谔方程的随机控制验证定理
DOI：
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发表时间：
2019
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通讯作者：
W. McEneaney
中科院分区：
文献类型：
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作者：
W. McEneaney
利用复值扩散过程，得到了薛定谔方程解的随机控制表示。采用Maslov反量化，其中域在空间变量中是复值的。利用平稳性的概念将去量子化薛定谔方程的Hamilton-Jacobi形式与其随机控制表示联系起来。不需要凸性，因此对问题的持续时间没有限制。此外，存在性减少到一个实值域的情况下。
A stochastic control representation for solution of the Schrödinger equation is obtained, utilizing complex-valued diffusion processes. The Maslov dequantization is employed, where the domain is complex-valued in the space variable. The notion of stationarity is utilized to relate the Hamilton–Jacobi form of the dequantized Schrödinger equation to its stochastic control representation. Convexity is not required, and consequently, there is no restriction on the duration of the problem. Additionally, existence is reduced to a real-valued domain case.