Definition (Jump time)

A jump time is a RV representing the first time after $n-1$ jumps that the state changes i.e. $$J_{n}=\inf\{t>J_{n-1}:X_{t}\not=X_{J_{n-1}}\}$$or the $n$-th jump time, $J_{n}$, is the first time, $t$, after the previous jump time, $J_{n-1}$, that the state changes.