For definite states \\(i, j \in D\\), define:

\\[H_{i,j} = (\Gamma_{i}'(0))(j)\\]

This is the instantaneous rate of change of the probability of being in state \\(j\\), given that the chain began in state \\(i\\).

Loosely speaking, it is the rate at which probability flows from definite state \\(i\\) to definite state \\(j\\).

\\[H_{i,j} = (\Gamma_{i}'(0))(j)\\]

This is the instantaneous rate of change of the probability of being in state \\(j\\), given that the chain began in state \\(i\\).

Loosely speaking, it is the rate at which probability flows from definite state \\(i\\) to definite state \\(j\\).