We consider next the continuous time dynamics of the Markov process (Xt)t∈R+ .
The dynamics is governed by a clock that rings randomly. The time interval τ be-
tween each of the clock ringing is exponentially distributed with parameter
P (τ t) = exp
Suppose that the clock rings at time t and that the process was in state x just before
the time t. The population x is transformed into the population y following the
same scheme as for the discrete time Markov chain (Xn)n∈N described previously.
At time t, the process jumps to the state y.