The conditional probabilities describing the movement from state to state of a Markov process {X_t, t ∈ T }. In general, the transition probabilities are written as Pr{X(t) ∈ A|X(s) = x} for times s < t in the time domain T and state x and event A in the state space. For a discrete-time Markov chain (DTMC) {X_n,0 ≤ n}, the transition probabilities are Pr{X_n+1 = j|X_n = i} = p_ij, for time n in the time domain and states i and j in the space state.  Markov chains;  Markov processes.