相依概率性序列运算的数字特征

Numerical characteristics of dependent probabilistic sequence operations

相依概率性序列运算对基本序列运算进行了发展,使非独立的随机变量间的建模、分析以及运算成为可能。该文证明了非独立的概率性序列进行各种序列运算后的派生序列仍然是概率性序列。研究了序列独立与非独立情形下各种运算结果序列期望值的异同,同时论证了在序列非独立情形下序列运算期望值的性质:一部分基本序列运算期望值性质在相依概率性序列运算中仍然成立,而另一部分则不再成立。利用简单算例验证了上述数字特征,并阐述了相依概率性序列运算的物理意义。

Dependent probabilistic sequence operations （DPSO） develops the basic probabilistie sequence operation （PSO） theory to facilitate modeling, analysis and operations of dependent stochastic variables. This theoretical study of the DPSO characteristics proves that sequences derived from DPSO are also probabilistic sequences. The differences on the expected values of the derived sequences with and without dependence are studied for each kind of DPSO. The relationships between the expected values of the derived sequences for different kinds of DPSO are also proved, with some PSO relationships still holding in DPSO while some no longer hold. A simple case study validates the numerical characteristics and explains their physical meaning.