论文标题
通过量子力学生成M-差异概率密度
Generating M-indeterminate probability densities by way of quantum mechanics
论文作者
论文摘要
并非由其时刻确定的概率密度被认为是“瞬间的”或“ m-dranderminate”。确定密度是否是差异性的，还是如何产生m-差异密度，这是悠久历史的挑战性问题。量子力学本质上是概率的，但是与标准概率理论相比，获得的概率密度截然不同，涉及复杂的波函数和操作员，以及其他方面。然而，最终结果是标准概率数量，例如期望值，力矩和概率密度函数。我们表明，获得密度的量子力学程序会导致一种简单的方法，以生成无限数量的M-模型密度。不同的自我接合操作员可以导致新的M-模型密度。根据操作员，该方法可以产生stieltjes类或不属于stieltjes类的新配方的密度。因此，该方法补充并扩展了现有方法，并为进一步发展开辟了新的途径。该方法适用于连续和离散的概率密度。给出了许多示例。
Probability densities that are not uniquely determined by their moments are said to be "moment-indeterminate", or "M-indeterminate". Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison to standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.
