The Poisson process was discovered by Simeon-Denis Poisson (1781-1840) and describes a statistic point process of
single events which occur ramdom in time.
An example for a possion process is the decay of some types of radioactive isotopes.
The Poisson distribution is given by
denotes the discret propability that occurs given the expectation value .
For a example how the Poisson distribution looks like for different values of see the following graph.
The joint probability distribution of n independent Poisson processes is
The Poisson process as biological approximation
The examination of the cortex showed that the neural response-properties are highly variable [1,2,3,5,6]. The observed
interspike-interval-distribution  looks like the exponential interevent-distribution (the interevent-distribution
defines the propability of the time-interval-length between two events) of the Poisson process.
The Poisson process and the tuning-function
and the Poisson process are connected through
the expectation value . The tuning-function
multiplied with the
size of the timewindow is used as the mean spikerate for the Poisson process.
 Britten KH, Shadlen MN, Newsome WT, Movshon JA (1993)
Responses of neurons in macaque MT to stochastic motion signals.
Vis Neurosci 10:1157-1169
 Burns BD, Webb AC (1976)
The spontaneous activity of neurones in the cat's cerebral cortex.
 Snowden RJ, Treue S, Andersen RA (1992)
The response of neurons in areas V1 and MT of the alert rhesus monkey to moving random dot patterns.
Exp Brain Res 88:389-400
 Softky W.R. , Koch C. (1993)
The highly irregular fireing of cortical cells is inconsistent with temporal integration of random EPSPs
Journal of Neuroscience, 13:334-350
 Tollhurst DJ, Movshon JA, Dean AF (1983)
The statistical reliability of signals in single neurons in cat and monkey visual cortex.
Vision Res 23:775-785
 Tomko, G., Crapper, D. (1974)
Neuronal variability: non-stationary responses to identical visual stimuli.
Brain Res 79:405-418