Given a continuous-time process $\{X_{t}:t\in[0,\infty)\}$ and its jump times, $\{J_{n}:n\ge0\}$, we define the holding times, $\{S_{n}:n\ge1\}$, as the time spent at each state between jumps or $$S_{n}=J_{n}-J_{n-1}, \ \mbox{for }n\ge1$$ ## Intuition Recall exponential RVs. $S_{n}\sim\mbox{Exp}$ because the exponential RV models the “waiting time” between events.