Point process
From Wikipedia, the free encyclopedia
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. The term point process is also sometimes used to mean random measure.
[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 
