Hi, please can someone tell me how to interpret lamba(i) in the holding time distribution in terms of transition rates (as opposed to the trivial definition as a parameter of the exponential distribution). It seems to be the instantaneous probability of leaving state i for any other state j not equal to i. is this correct?
If by "instantaneous probability" you mean "force of transition", then yes. lambda_i(t) is the total force of transition out of state i at time t. If the process is time-homogeneous, you can drop the t as the forces will then all be constant.
