映射族的推移算子及其在随机过程中的应用

该文研究很一般化的映射族的推移算子.设参数集T＝0,+∞)或T＝{0，1， 2，…}，以及任意非空的集合Ω和E，Ω和E均不配置可测σ代数，更不配置测度或概率.在 引进δ映射和δ代数的基础上，研究了Ω到E的映射族X＝｛X(t),t∈T∩［0，σ)｝(σ∈T ∪｛+∞｝)存在推移算子的充分必要条件.讨论了推移算子的诸多性质，以及推移算子在随机过程中的应用。

Shift Operators of Map Family and Its Application to Stochastic Processes

The authors researched the shift operators of map family in vague ge neralizati on. Given a parameter set T=［0，+∞) or T=｛0，1，2，…｝,and two arbit rary non empty sets Ω and E,which are not disposed any measurable σ algebra and  any measure.The set of all maps φ： T∩［0，β)→E,where β∈T∪｛＋∞｝, is deno ted by  Ω (E). The map X:   Ω→Ω(E) is a map family X=｛X(t),t∈T∩［0， σ)｝ in fact. It is followed that the necessary and sufficient condition of existence for shift  operators of a map family X=｛X(t),t∈T∩［0，σ)｝.  Some properties  of shift operators and some applications to stochastic processes for shift opera tors are discussed.