12

RAPHA¨

EL CERF

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

m2λ:

∀t ∈

R+

P (τ t) = exp

(

−

m2λt

)

.

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.