Suppose matrix Q = (qij), i,j E, E = {1,2,...}, then 0 < qij < , i j, v qi1 4 qi < co,qi -- Zqlj 3 0, which is called a quasi -- 0 -- matrix.Let matrix p(t) = ] / t , (pg.(t), t 3 0, then p,(t) 3 0, Zp,(t) $1...Suppose matrix Q = (qij), i,j E, E = {1,2,...}, then 0 < qij < , i j, v qi1 4 qi < co,qi -- Zqlj 3 0, which is called a quasi -- 0 -- matrix.Let matrix p(t) = ] / t , (pg.(t), t 3 0, then p,(t) 3 0, Zp,(t) $1,pn(t + s) = cp.(t)p^j(s), ltepi).(t) = j k {0: i = j, wich is called a homogeneous enumehole Marrov process (transition matrix). for a .. given quasi -- Q -- maaed Q, the three qllestions allse: ac Does there exist a Q -- process wilh Q as its density matrix (i. e. p’,(0) = qij )? @If so, what are necessey and sufficient conditions for the Q -- process to be unique? @If ac is valid, give all the P(t ) s ? The above three issues are called "Construction Theory". The progress and the remaining problem are to be elaborated, with its applications illustrated.展开更多
文摘Suppose matrix Q = (qij), i,j E, E = {1,2,...}, then 0 < qij < , i j, v qi1 4 qi < co,qi -- Zqlj 3 0, which is called a quasi -- 0 -- matrix.Let matrix p(t) = ] / t , (pg.(t), t 3 0, then p,(t) 3 0, Zp,(t) $1,pn(t + s) = cp.(t)p^j(s), ltepi).(t) = j k {0: i = j, wich is called a homogeneous enumehole Marrov process (transition matrix). for a .. given quasi -- Q -- maaed Q, the three qllestions allse: ac Does there exist a Q -- process wilh Q as its density matrix (i. e. p’,(0) = qij )? @If so, what are necessey and sufficient conditions for the Q -- process to be unique? @If ac is valid, give all the P(t ) s ? The above three issues are called "Construction Theory". The progress and the remaining problem are to be elaborated, with its applications illustrated.
