Module 2:Poisson Process and Kolmorogov equations
  Lecture 7:Poisson Process Continued
 

Property 2.4

Difference of two independent Poisson process will NOT be Poisson process.

Derivation of correlation coefficient of Poisson process


Suppose  is a Poisson process with rate , then the correlation coefficient between  and  is given by .

Proof

We know that , ,  and .

Furthermore we know that:

 

                  

                  

                  

                  


                  

                                        

Note

This correlation is known as auto-correlation.