The conditional intensity 
associated to a temporal
point process 
is defined to be the expected infinitesimal rate at which events are expected to
occur around time 
given the history of 
at times prior to time 
. Algebraically,
![lambda(t)=lim_(Deltat->0)(E[N(t,t+Deltat)|H_t])/(Deltat),](/anna-https-mathworld.wolfram.com/images/equations/ConditionalIntensityFunction/NumberedEquation1.svg) |
where ![E[Y|H_t]](/anna-https-mathworld.wolfram.com/images/equations/ConditionalIntensityFunction/Inline6.svg)
denotes the expectation value of 
given 
. The limit is assumed to exist,
and 
is the history of 
over all times strictly prior to time 
.
