非交换概率空间上的切比雪夫不等式与大数定理

Tchebycheff's Inequality and Law of Large Numbers over Noncommutative Probability Spaces

研究了非交换概率空间上自伴随机变量的期望、方差、独立性、相关性等性质,证明了关于自伴随机变量的切比雪夫不等式与大数定理。

We study in this paper the expectation, variance, independence and linear dependence of self-adjoint random variables on a noncommutative probability space, and prove Tchebycheff inequality and law of large numbers. We also give a necessary and sufficient condition for two self-adjoint random variables to be linearly dependent.