Editing Stochastic process (section)

====Poisson process====
The Poisson process is named after [[Siméon Poisson]], due to its definition involving the [[Poisson distribution]], but Poisson never studied the process.<ref name="Stirzaker2000"/><ref name="DaleyVere-Jones2006page8">{{cite book|author1=D.J. Daley|author2=D. Vere-Jones|title=An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods|url=https://books.google.com/books?id=6Sv4BwAAQBAJ|year=2006|publisher=Springer Science & Business Media|isbn=978-0-387-21564-8|pages=8–9}}</ref> There are a number of claims for early uses or discoveries of the Poisson
process.<ref name="Stirzaker2000"/><ref name="GuttorpThorarinsdottir2012"/>
At the beginning of the 20th century, the Poisson process would arise independently in different situations.<ref name="Stirzaker2000"/><ref name="GuttorpThorarinsdottir2012"/>
In Sweden 1903, [[Filip Lundberg]] published a [[thesis]] containing work, now considered fundamental and pioneering, where he proposed to model insurance claims with a homogeneous Poisson process.<ref name="EmbrechtsFrey2001page367">{{cite book|last1=Embrechts|first1=Paul|title=Stochastic Processes: Theory and Methods|last2=Frey|first2=Rüdiger|last3=Furrer|first3=Hansjörg|chapter=Stochastic processes in insurance and finance|volume=19|year=2001|page=367|issn=0169-7161|doi=10.1016/S0169-7161(01)19014-0|series=Handbook of Statistics|isbn=978-0444500144}}</ref><ref name="Cramér1969">{{cite journal|last1=Cramér|first1=Harald|title=Historical review of Filip Lundberg's works on risk theory|journal=Scandinavian Actuarial Journal|volume=1969|issue=sup3|year=1969|pages=6–12|issn=0346-1238|doi=10.1080/03461238.1969.10404602}}</ref>

Another discovery occurred in [[Denmark]] in 1909 when [[A.K. Erlang]] derived the Poisson distribution when developing a mathematical model for the number of incoming phone calls in a finite time interval. Erlang was not at the time aware of Poisson's earlier work and assumed that the number phone calls arriving in each interval of time were independent to each other. He then found the limiting case, which is effectively recasting the Poisson distribution as a limit of the binomial distribution.<ref name="Stirzaker2000"/>

In 1910, [[Ernest Rutherford]] and [[Hans Geiger]] published experimental results on counting alpha particles. Motivated by their work, [[Harry Bateman]] studied the counting problem and derived Poisson probabilities as a solution to a family of differential equations, resulting in the independent discovery of the Poisson process.<ref name="Stirzaker2000"/> After this time there were many studies and applications of the Poisson process, but its early history is complicated, which has been explained by the various applications of the process in numerous fields by biologists, ecologists, engineers and various physical scientists.<ref name="Stirzaker2000"/>