Editing Markov chain (section)

====Infinitesimal definition====
[[File:Intensities_vs_transition_probabilities.svg|thumb|The continuous time Markov chain is characterized by the transition rates, the derivatives with respect to time of the transition probabilities between states i and j.]]
Let <math>X_t</math> be the random variable describing the state of the process at time ''t'', and assume the process is in a state ''i'' at time ''t''. 
Then, knowing <math>X_t = i</math>, <math>X_{t+h}=j</math> is independent of previous values <math>\left( X_s : s < t \right)</math>, and as ''h'' → 0 for all ''j'' and for all ''t'',
<math display="block">\Pr(X(t+h) = j \mid X(t) = i) = \delta_{ij} + q_{ij}h + o(h),</math>
where <math>\delta_{ij}</math> is the [[Kronecker delta]], using the [[little-o notation]].
The <math>q_{ij}</math> can be seen as measuring how quickly the transition from ''i'' to ''j'' happens.