Superpositions of probability distributions.
Superpositions of probability distributions.
复制标题
概率分布的叠加。
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
H. Kleinert
中科院分区：
文献类型：
--
作者：
P. Jizba;H. Kleinert
概率分布是由不同方差的高斯分布叠加而成的，在量子理论和金融市场中有着广泛的应用。对于马尔可夫过程，这种叠加不一定要遵守Chapman-Kolmogorov半群关系，因为它们可能会引入记忆效应。在不破坏半群性质的前提下，我们得到了v中拖尾分布的一般形式。涂抹技术有两个直接的应用。它可以简化涂抹和非涂抹条件概率的Kramers-MoYal方程组，并且可以方便地在路径积分学中实现。在许多情况下，路径积分的叠加比初始路径积分容易得多。给出了三个简单的例子，并展示了如何将该技术扩展到量子力学。
Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances v=sigma;{2} play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian processes because they may introduce memory effects. We derive the general form of the smearing distributions in v which do not destroy the semigroup property. The smearing technique has two immediate applications. It permits simplifying the system of Kramers-Moyal equations for smeared and unsmeared conditional probabilities, and can be conveniently implemented in the path integral calculus. In many cases, the superposition of path integrals can be evaluated much easier than the initial path integral. Three simple examples are presented, and it is shown how the technique is extended to quantum mechanics.