Point process
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A point process is a type of stochastic process that is widely used in many fields of applied mathematics, such as queueing theory and computational neuroscience.
[edit] Definition
A point process is a map 
from a probability space Ω to a set K consisting of finite subsets of a metric space X.
In applied mathematics the space X is usually the real line, which is often interpreted as time. Thus a collection of points in X may be interpreted as a sequence of event times, and for each outcome 
is a sequence of event times 
, where the number N of event times may be different for different 
[edit] conditional intensity function
A conditional intensity function of a point process is a function 
defined as
![\lambda(t| H_{t})=\lim_{\Delta t\to 0}\frac{1}{\Delta t}{P}(\mbox{One spike occurs in the time-interval}\,[t,t+\Delta t]\,|\, H_t) ,](../../../math/c/a/8/ca8e5449d07024b7c0fac9aaec056b06.png)
where 
denotes the history of event times preceding time 
