区间值马氏过程

Interval-valued Markov Processes

设 (Ω ,A,P)为完备概率空间 ,{ξt,t 0 }、{ηt,t 0 }为 Rm中取值的向量值随机过程 ,且ξt ηt,t 0 ,本文证明 :当 {ξt,t 0 }与 {ηt,t 0 }相互独立时 ,1区间值随机过程 {[ξt,ηt],t 0 }为马氏过程的充要条件是 {ξt,t 0 },{ηt,t 0 }分别为马氏过程。2若 {[ξt,ηt],t 0 }为区间值马氏过程 ,则存在向量值马氏选择过程 ;若 {[ξt,ηt],t 0 }为区间值马氏链 ,则表示定理成立。

Let｛ξ t,t0｝,｛η t,t0｝be two R m valued stochastic processes,ξ tη t t0.In this paper,we obtain the following results,if ｛ξ t,t0｝ and｛η t,t0｝ are independence,then ① interval valued process ｛[ξ t,η t],t0｝ be Markov process iff ｛ξ t,t0｝ and ｛η t,t0｝ are all Markov processes;② If ｛[ξ t,η t],t0｝ is Markov processes,it exists the Markov selections,if ｛[ξ t,η t],t0｝ is Markov chain,the Markov representation theorem is established.