概率性序列运算的扩展及其运算性质

Extensions and properties of probabilistic sequence operations

现有序列运算理论的核心是卷和、卷差、交积与并积运算等4个基本运算。当面对连续型随机变量延伸至离散型概率性序列时,为了提高概率性序列运算理论的适用性,该文提出了序乘运算、序除运算及序移运算等新的概率性序列运算形式,用于处理概率性序列之间以及序列与正常数之间的乘、除等关系,并推导出各种基本运算的基本性质,分析了这几种运算的物理意义。算例结果表明了运算性质的正确性。

Addition-type convolution, subtraction type convolution, AND-type products and OR-type products are four basic operations in sequence operation theory. The applicability of probabilistic sequence operation theory was extended by several new basic operations for sequence multiplication, sequence division and sequence shift operations for multiplication and division of sequences, as well as sequences and positive constants with continuous random variables extending to discrete probabilistic sequences. The basic nature and physical meaning of these operations were given. A case study shows the rationality of these probabilistic sequence operations.