Stochastic calculus of variations and mechanics

Stochastic calculus of variations and mechanics
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随机变分法和力学

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发表时间：
1983
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影响因子：
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通讯作者：
W. Fleming
W. Fleming
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文献类型：
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作者：
W. Fleming

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考虑了含势项热方程（薛定谔方程的虚时间模拟）的柯西问题。经过对数变换后，该柯西问题的正解转化为随机变分问题的动态规划方程的解。后一个问题是一个最不平均的行动。当适当的参数趋于零时，得到经典的最小作用原理。
The Cauchy problem for the heat equation with a potential term (imaginary time analogue of the Schrodinger equation) is considered. After a logarithmic transformation, a positive solution to this Cauchy problem turns into a solution to the dynamic programming equation for a problem of stochastic calculus of variations. The latter problem is one of least average action. The classical principle of least action is obtained as an appropriate parameter tends to zero.