设对每一正数t, E(t)和A(t)是不相交事件,分别以J_1(t),J_2(t),J_2(t)记E(t)A(t),E(t)UA(t),以J(t,L)记(?)J_l(t),其中L(?){1,2,3}。如果对任意的0<t_1<…<t_(i+g),都有P(J(t_1,L_1)…J(t_(i-1),L_(i-1))E(t_i)J(t_(i+1),L_(i+...设对每一正数t, E(t)和A(t)是不相交事件,分别以J_1(t),J_2(t),J_2(t)记E(t)A(t),E(t)UA(t),以J(t,L)记(?)J_l(t),其中L(?){1,2,3}。如果对任意的0<t_1<…<t_(i+g),都有P(J(t_1,L_1)…J(t_(i-1),L_(i-1))E(t_i)J(t_(i+1),L_(i+1))…J(t_(i+g),L_(i+g))=P(J(t_1,L_1)…J(t_(i-1),L_(i-1))E(t_i))P(J(t_(i+1)一t_i,L_(i+1))…J(t_(i+g)-t_i,L_(i+g)),则称{(E(t),A(t)):t>0}是(?)再生现象,(p(t),a(t))是对应的P-a对,其中p(t):=P(E(t)),a(t):=P(A(t))设(?)p(t)=1 则(p(t),a(t))是p-a对当且仅当存在Markov转移函数P_t(·,·),标准状态x,可测集B,x(?)B,使P(t)=P_t,(x,{x}),a(t)=P_t(x,B);当且仅当a(t)连续,p(t)是p函数(设有典型测度μ),存在可测函数g(s)满足0≤g(s)≤μ(s,∞]和a(t)=integral from n=0 to t(p(t-s)g(s)ds).p-a对的积和极限仍为p-a对.给出p-a对为有限可分解和为不可分解的充分条件.展开更多
文摘设对每一正数t, E(t)和A(t)是不相交事件,分别以J_1(t),J_2(t),J_2(t)记E(t)A(t),E(t)UA(t),以J(t,L)记(?)J_l(t),其中L(?){1,2,3}。如果对任意的0<t_1<…<t_(i+g),都有P(J(t_1,L_1)…J(t_(i-1),L_(i-1))E(t_i)J(t_(i+1),L_(i+1))…J(t_(i+g),L_(i+g))=P(J(t_1,L_1)…J(t_(i-1),L_(i-1))E(t_i))P(J(t_(i+1)一t_i,L_(i+1))…J(t_(i+g)-t_i,L_(i+g)),则称{(E(t),A(t)):t>0}是(?)再生现象,(p(t),a(t))是对应的P-a对,其中p(t):=P(E(t)),a(t):=P(A(t))设(?)p(t)=1 则(p(t),a(t))是p-a对当且仅当存在Markov转移函数P_t(·,·),标准状态x,可测集B,x(?)B,使P(t)=P_t,(x,{x}),a(t)=P_t(x,B);当且仅当a(t)连续,p(t)是p函数(设有典型测度μ),存在可测函数g(s)满足0≤g(s)≤μ(s,∞]和a(t)=integral from n=0 to t(p(t-s)g(s)ds).p-a对的积和极限仍为p-a对.给出p-a对为有限可分解和为不可分解的充分条件.
