Content deleted Content added
Line 98:
On the real line, the homogeneous Poisson point process has a connection to the theory of [[martingale (probability theory)|martingale]]s via the following characterization: a point process is the homogeneous Poisson point process if and only if
:<math> N(-\infty,t]-\lambda t, </math>
is a martingale.<ref name="merzbach1986characterization">E. Merzbach and D. Nualart. A characterization of the spatial poisson process and changing time. ''The Annals of Probability'', 14(4):1380–1390, 1986.</ref><ref>{{cite journal | url=https://www.jstor.org/stable/3212898 | jstor=3212898 | title=On the Characterization of Point Processes with the Order Statistic Property | last1=Feigin | first1=Paul D. | journal=Journal of Applied Probability | year=1979 | volume=16 | issue=2 | pages=297–304 | doi=10.2307/3212898 | s2cid=123904407 }}</ref>
| |||