Constraining the First Hitting Time

Let X(ω)= {x(t, ω), t≥0} be Markov chains with stationary, defined tm complete probability space (Ω,P). The transition probabitity matrix {p_(ij)(t):t≥0,i,j∈I} is sta ndard and satisfies the forward equations, where I={0, 1, 2,…} is the state space of X(ω). All states of X(ω) are stable. The sample functions are right lower semicontinuous. The Q-matrix is conservative. The X(ω) is Borel measurable and well separate. The condition (C) is true. (cf, 1])